{"id":14274,"date":"2022-12-15T10:34:52","date_gmt":"2022-12-15T10:34:52","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=14274"},"modified":"2024-10-07T11:05:38","modified_gmt":"2024-10-07T11:05:38","slug":"square-and-square-roots","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots","title":{"rendered":"Square and Square Roots"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-f8bc4a7b-e18c-49ef-8aad-e49487707e32\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots#0-what-are-squares-and-square-roots>What Are Squares and Square Roots?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots#4-what-are-perfect-squares>What Are Perfect Squares?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots#9-how-to-find-the-square>How to Find the Square<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots#11-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots#12-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots#13-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-squares-and-square-roots\">What Are Squares and Square Roots?<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-1.png\" alt=\"Square root of 9\" class=\"wp-image-14291\" title=\"Square root of 9\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-1.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-1-300x196.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">When you multiply a number by itself, you get the square of a number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For instance, $3 \\times 3 = 9$. So, the square of 3 is 9.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Square root goes the other way round. If the square of 3 is 9, then the square root of 9 is 3.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, we can say that <strong>square and square roots<\/strong> are inverse operations of each other.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-squares-and-trapezoids-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_square_trapezoid_2_pt.png\" alt=\"Classify Squares and Trapezoids as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Squares and Trapezoids as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/evaluate-algebraic-expressions-with-one-operation\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_evaluate_algebric_exp_1_pt.png\" alt=\"Evaluate Algebraic Expressions with One Operation Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Evaluate Algebraic Expressions with One Operation Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/evaluate-algebraic-expressions-with-two-operations\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_evaluate_algebric_exp_2_pt.png\" alt=\"Evaluate Algebraic Expressions with Two Operations Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Evaluate Algebraic Expressions with Two Operations Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-area-in-square-units\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_1_2_gm.png\" alt=\"Find Area in Square Units Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Area in Square Units Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-area-with-unit-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_square_2_pt.png\" alt=\"Find the Area with Unit Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Area with Unit Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/form-algebraic-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_choose_exp_1_pt.png\" alt=\"Form Algebraic Expressions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Form Algebraic Expressions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-kite-squares-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_square_rectangle_pt.png\" alt=\"Identify Kite, Squares and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Kite, Squares and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-squares-and-trapezoids\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_19_21_gm.png\" alt=\"Identify Squares and Trapezoids Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Squares and Trapezoids Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-how-to-define-square-and-square-root\">How to Define Square and Square Root<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"371\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-2.png\" alt=\"Symbol of square root\" class=\"wp-image-14293\" title=\"Symbol of square root\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-2-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"2-square-of-a-number-\"><strong>Square of a Number<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">A square is a number obtained by multiplying the number by itself. If $n$ is a number, then its square is represented by $n$ raised to the power 2, i.e., $n^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example:<\/p>\n\n\n\n<ul class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\">Square of $1 = 1^2 = 1 \\times 1 = 1$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Square of $4 = 4^2 = 4 \\times 4 = 16$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Square of $5.5 = (5.5)^2 = 5.5 \\times 5.5 = 30.25$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">We can also find the square of a negative number. For example: $(\u22124) \\times (\u22124) = 16$.<\/p>\n\n\n\n<p>Did you notice that the squares of 4 and $(\u22124)$ are the same? This happens because squaring any number always gives a positive result. Anything negative squared becomes a positive value. So, squaring a positive number and its negative counterpart will provide the same outcome.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-square-root-of-a-number-\"><strong>Square Root of a Number<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The square root of a number is the value that, when multiplied by itself, gives the original number. For example, both $+\\;5$ and $-\\;5$ are square roots of 25 because:<\/p>\n\n\n\n<p>$5 \\times 5 = 25$<\/p>\n\n\n\n<p>$(-\\;5) \\times (-\\;5) = 25$<\/p>\n\n\n\n<p>Thus, every positive real number n has two square roots\u2014a positive square root\u00a0 $(\\sqrt{n})$ and a negative square root $(-\\sqrt{n})$. The unique positive square root $\\sqrt{n}$ is called the principal square root or principal root.<\/p>\n\n\n\n<p>The radical sign (\u221a) generally represents the principal square root. For instance, the principal square root of 25 is written as $\\sqrt{25}$.\u00a0<\/p>\n\n\n\n<p>$\\sqrt{25} = 5$<\/p>\n\n\n\n<p>We refer to -5 as the negative square root of 25.<\/p>\n\n\n\n<p>Unless specified otherwise, &#8220;the square root&#8221; of a number refers exclusively to the principal square root.&nbsp; Thus,&nbsp;&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\sqrt{49} = 7$<\/li>\n\n\n\n<li>$\\sqrt{36} = 6$<\/li>\n<\/ul>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/squares-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/squares-and-circles.jpeg\" alt=\"Squares and Circles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-what-are-perfect-squares\">What Are Perfect Squares?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A <strong>perfect square<\/strong> is a number obtained by multiplying an integer with itself. An integer does not contain fractions or decimals.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here\u2019s a <strong>square roots chart<\/strong> of the first ten <strong>perfect squares. <\/strong>It shows positive square roots of the given perfect square.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"850\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-3.png\" alt=\"Perfect Squares\" class=\"wp-image-14294\" title=\"Perfect Squares\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-3-219x300.png 219w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">As you can see, only a few numbers are perfect squares. The rest of the numbers are imperfect squares. The square root of imperfect squares contains fractions and decimals.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example:<\/p>\n\n\n\n<ul class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\">$\\sqrt{10} = 3.163$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\sqrt{20} = 4.472$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-different-methods-of-finding-square-root\">Different Methods of Finding Square Root<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are various ways to find the square root of a number. Let\u2019s look at some of the commonly used methods:<\/p>\n\n\n\n<ul class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\">Repeated Subtraction Method<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Prime Factorization Method<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Long Division Method<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-repeated-subtraction-method-\"><strong>Repeated Subtraction Method<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Here\u2019s how to find the square root of a number using this method:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: <\/strong>Take the number and subtract consecutive odd numbers from it till you reach zero.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>The number of times you subtract is the square root of the number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s take 25, for example. So, subtracting consecutive odd numbers from it, we get:<\/p>\n\n\n\n<ol class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\">$25 \u2212 1 = 24$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$24 \u2212 3 = 21$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$21 \u2212 5 = 16$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$16 \u2212 7 = 9$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$9 \u2212 9 = 0$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">Here, we subtracted five times. So the square root of 25 is 5. Isn\u2019t that cool?<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-prime-factorization-method-\"><strong>Prime Factorization Method<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s say you want to find the square root of 1764. Here\u2019s how to find it using the factorization method:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: Find the prime factors of 1764.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-4.png\" alt=\"Prime factors of 1764\" class=\"wp-image-14295\" title=\"Prime factors of 1764\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-4-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;So, $1764 = 2 \\times 2 \\times 3 \\times 3 \\times 7 \\times 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: Form pairs of similar factors.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we can make three pairs of similar factors.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\underline{2 \\times 2} \\times \\underline{3 \\times 3} \\times \\underline{7 \\times 7}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: Take one from each pair and find their product.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2 \\times 3 \\times 7 = 42$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: The product is the square root of the number.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, $\\sqrt{1764} = 42$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note: If the number does not make a pair of similar factors we place them inside the square root symbol.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, to find the square root of 8.<\/p>\n\n\n\n<ol class=\"wp-block-list eplus-wrapper\">\n<li class=\"eplus-wrapper\"><strong>Find the prime factors of 8.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-5.png\" alt=\"Prime factors of 8\" class=\"wp-image-14296\" title=\"Prime factors of 8\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-5-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: Form pairs of similar factors.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we can make two pairs of similar factors<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\underline{2 \\times 2} \\times 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: Take one from the pair and place it outside the square root symbol<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, $\\sqrt{8} = 2\\sqrt{2}$.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"8-long-division-method-\"><strong>Long Division Method<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s say we need to find the square root of 529 using the long division method.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Place a bar over every pair of digits of 529, starting from the right.<\/p>\n\n\n\n<figure class=\"wp-block-image eplus-wrapper\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Vn8xg3HhkAV60sENdfF8ftknCUeGV4_YFp6E86ScphzBtlcRDSoAxgV6BFFJy6geO5TsGH2TemY95P6wy5JyUOUFnCWyrBZ5oCkeDYy5aQCQmGTccwCDn4gQrY7h5VhzQQLSAUSA8KS3GnH-Pc_XfDyGg2FtfzqJItsHBwVpO5Mxry5YhSJm5OfPgg2i4Q\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> Take the leftmost number and divide it by the largest number whose square is less than or equal to the leftmost pair.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the leftmost number is 5. We are dividing it by 2 because the square of 2 is 4, which is less than five.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"525\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-6.png\" alt=\"The square root of 529 Step 1\" class=\"wp-image-14297\" title=\"The square root of 529 Step 1\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-6-300x254.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> Bring down the other pair to the right of the remainder.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"405\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-7.png\" alt=\"Square root of 529 Step 2\" class=\"wp-image-14298\" title=\"Square root of 529 Step 2\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-7-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4:<\/strong> Add the quotient to the divisor and enter it with a blank space on the right.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"475\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-8.png\" alt=\"Square root of 529 Step 3\" class=\"wp-image-14299\" title=\"Square root of 529 Step 3\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-8.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-8-300x230.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 5:<\/strong> Find the suitable number for the unit digit of the divisor. The number should be such that when multiplied by the new digit, it should be equal to or less than the dividend.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this case, $43 \\times 3 = 129$. So, the number to be added should be 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"458\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-9.png\" alt=\"Square root of 529\" class=\"wp-image-14300\" title=\"Square root of 529\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-9.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-9-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 6: <\/strong>The remainder is zero. So the answer is 23.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, $\\sqrt{529} = 23$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can find the square root of an imperfect square as well using the long division method.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, the square root of 10 is 3.16.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"707\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-10.png\" alt=\"Square root of 10\" class=\"wp-image-14301\" title=\"Square root of 10\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-10.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/What-is-Square-and-square-roots-10-263x300.png 263w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-how-to-find-the-square\">How to Find the Square<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Finding the square of a number is comparatively easier than finding the square root.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">You can simply use the multiplication table to find the square of a single-digit number. For a two-digit number, you can multiply by the number by itself to get the answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$6 \\times 6 = 36$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$125 \\times 125 = 15,625$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">So these are some of the different <strong>square root tips and tricks<\/strong>. Once you understand the method, <strong>dividing and multiplying square roots<\/strong> becomes really easy. You can now use these concepts to solve various problems related to square roots. Have fun!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Find the square root of 144 using the subtraction method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Subtracting consecutive odd numbers from it, we get:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"281\" height=\"766\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-1-1.png\" alt=\"Repeated subtraction of 144\" class=\"wp-image-14302\" title=\"Repeated subtraction of 144\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-1-1.png 281w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-1-1-110x300.png 110w\" sizes=\"auto, (max-width: 281px) 100vw, 281px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Here, we subtracted twelve times. So the square root of 144 is 12.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the square root of 7056 using the prime factorization method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"354\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-2-2.png\" alt=\"Prime factors of 7056\" class=\"wp-image-14303\" title=\"Prime factors of 7056\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-2-2.png 355w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-2-2-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-2-2-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-2-2-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-2-2-120x120.png 120w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">$7056 = 2 \\times 2 \\times 2 \\times 2 \\times 3 \\times 3 \\times 7 \\times 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{7056} = 2 \\times 2 \\times 3 \\times 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 84$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Find the square root of 1764 using the long division method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-3-1.png\" alt=\"Square root of 1764\" class=\"wp-image-14304\" title=\"Square root of 1764\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-3-1.png 355w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-3-1-285x300.png 285w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The square root of 1764 is 42.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Check whether 24 is a perfect square.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"354\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-4-1.png\" alt=\"Prime factors of 24\" class=\"wp-image-14305\" title=\"Prime factors of 24\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-4-1.png 355w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-4-1-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-4-1-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-4-1-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Solved-Examples-4-1-120x120.png 120w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$24 = 2 \\times 2 \\times 2 \\times 3<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{24} = 2\\sqrt{2} \\times \\sqrt{3} = 2\\sqrt{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{24} = 2\\sqrt{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, 24 is not a perfect square.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Find the value of <\/strong>$\\sqrt{36} + \\sqrt{625}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{36} = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{625} = 25$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $\\sqrt{36} + \\sqrt{625} = 6 + 25 = 31$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Square and Square Roots<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the square root of 121 using the repeated subtraction method.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8<\/div><div class=\"spq_answer_block\" data-value=\"1\">9<\/div><div class=\"spq_answer_block\" data-value=\"2\">10<\/div><div class=\"spq_answer_block\" data-value=\"3\">11<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 11<br\/>$121 \u2013 1 = 120$<br>\r\n$120 \u2013 3 = 117$<br>\r\n$117 \u2013 5 = 112$<br>\r\n$112 \u2013 7 = 105$<br>\r\n$105 \u2013 9 = 96$<br>\r\n$96 \u2013 11 = 85$<br>\r\n$85 \u2013 13 = 72$<br>\r\n$72 \u2013 15 = 57$<br>\r\n$57 \u2013 17 = 40$<br>\r\n$40 \u2013 19 = 21$<br>\r\n$21 \u2013 21 = 0$<br>\r\nTherefore, the square root of 121 is 11.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find the square root of 4096 using the factorization method.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">32<\/div><div class=\"spq_answer_block\" data-value=\"1\">48<\/div><div class=\"spq_answer_block\" data-value=\"2\">64<\/div><div class=\"spq_answer_block\" data-value=\"3\">72<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 64<br\/>So, $4096 = \\underline{2\\times2} \\times \\underline{2\\times2} \\times \\underline{2\\times2} \\times \\underline{2\\times2} \\times \\underline{2\\times2} \\times \\underline{2\\times2}$<br>\r\n$\\sqrt{4096} = 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 = 64$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-1-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find the square root of 1000 using the long division method.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">100.66<\/div><div class=\"spq_answer_block\" data-value=\"2\">31.622<\/div><div class=\"spq_answer_block\" data-value=\"3\">109.99<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 31.622<br\/>Square root of 1000<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-2.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Find the square root of 2304 using the long division method.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">40<\/div><div class=\"spq_answer_block\" data-value=\"1\">42<\/div><div class=\"spq_answer_block\" data-value=\"2\">45<\/div><div class=\"spq_answer_block\" data-value=\"3\">48<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 48<br\/>Square root of 2304<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-3-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find the least number by which 1800 must be multiplied to make it a perfect square.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">4<\/div><div class=\"spq_answer_block\" data-value=\"3\">5<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 2<br\/>$1800 = 2 \u00d7 \\underline{2 \\times 2} \\times \\underline{5 \\times 5} \\times \\underline{3 \\times 3}$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$1800 \\times 2 = \\underline{2\\times2} \\times \\underline{2\\times2} \\times \\underline{5\\times5} \\times \\underline{3\\times3}$<br>\r\n$= 3600$<br>\r\n$\\sqrt{3600} = 2 \\times 2 \\times 5 \\times 3 = 60$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-4.png\"><\/div><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Square and Square Roots\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Square and Square Roots\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the square root of 121 using the repeated subtraction method.\",\n                    \"text\": \"Find the square root of 121 using the repeated subtraction method.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$121 \u2013 1 = 120$$<br>\r\n$$120 \u2013 3 = 117$$<br>\r\n$$117 \u2013 5 = 112$$<br>\r\n$$112 \u2013 7 = 105$$<br>\r\n$$105 \u2013 9 = 96$$<br>\r\n$$96 \u2013 11 = 85$$<br>\r\n$$85 \u2013 13 = 72$$<br>\r\n$$72 \u2013 15 = 57$$<br>\r\n$$57 \u2013 17 = 40$$<br>\r\n$$40 \u2013 19 = 21$$<br>\r\n$$21 \u2013 21 = 0$$<br>\r\nTherefore, the square root of 121 is 11.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$121 \u2013 1 = 120$$<br>\r\n$$120 \u2013 3 = 117$$<br>\r\n$$117 \u2013 5 = 112$$<br>\r\n$$112 \u2013 7 = 105$$<br>\r\n$$105 \u2013 9 = 96$$<br>\r\n$$96 \u2013 11 = 85$$<br>\r\n$$85 \u2013 13 = 72$$<br>\r\n$$72 \u2013 15 = 57$$<br>\r\n$$57 \u2013 17 = 40$$<br>\r\n$$40 \u2013 19 = 21$$<br>\r\n$$21 \u2013 21 = 0$$<br>\r\nTherefore, the square root of 121 is 11.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$121 \u2013 1 = 120$$<br>\r\n$$120 \u2013 3 = 117$$<br>\r\n$$117 \u2013 5 = 112$$<br>\r\n$$112 \u2013 7 = 105$$<br>\r\n$$105 \u2013 9 = 96$$<br>\r\n$$96 \u2013 11 = 85$$<br>\r\n$$85 \u2013 13 = 72$$<br>\r\n$$72 \u2013 15 = 57$$<br>\r\n$$57 \u2013 17 = 40$$<br>\r\n$$40 \u2013 19 = 21$$<br>\r\n$$21 \u2013 21 = 0$$<br>\r\nTherefore, the square root of 121 is 11.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$121 \u2013 1 = 120$$<br>\r\n$$120 \u2013 3 = 117$$<br>\r\n$$117 \u2013 5 = 112$$<br>\r\n$$112 \u2013 7 = 105$$<br>\r\n$$105 \u2013 9 = 96$$<br>\r\n$$96 \u2013 11 = 85$$<br>\r\n$$85 \u2013 13 = 72$$<br>\r\n$$72 \u2013 15 = 57$$<br>\r\n$$57 \u2013 17 = 40$$<br>\r\n$$40 \u2013 19 = 21$$<br>\r\n$$21 \u2013 21 = 0$$<br>\r\nTherefore, the square root of 121 is 11.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"11\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$121 \u2013 1 = 120$$<br>\r\n$$120 \u2013 3 = 117$$<br>\r\n$$117 \u2013 5 = 112$$<br>\r\n$$112 \u2013 7 = 105$$<br>\r\n$$105 \u2013 9 = 96$$<br>\r\n$$96 \u2013 11 = 85$$<br>\r\n$$85 \u2013 13 = 72$$<br>\r\n$$72 \u2013 15 = 57$$<br>\r\n$$57 \u2013 17 = 40$$<br>\r\n$$40 \u2013 19 = 21$$<br>\r\n$$21 \u2013 21 = 0$$<br>\r\nTherefore, the square root of 121 is 11.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$121 \u2013 1 = 120$$<br>\r\n$$120 \u2013 3 = 117$$<br>\r\n$$117 \u2013 5 = 112$$<br>\r\n$$112 \u2013 7 = 105$$<br>\r\n$$105 \u2013 9 = 96$$<br>\r\n$$96 \u2013 11 = 85$$<br>\r\n$$85 \u2013 13 = 72$$<br>\r\n$$72 \u2013 15 = 57$$<br>\r\n$$57 \u2013 17 = 40$$<br>\r\n$$40 \u2013 19 = 21$$<br>\r\n$$21 \u2013 21 = 0$$<br>\r\nTherefore, the square root of 121 is 11.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the square root of 4096 using the factorization method.\",\n                    \"text\": \"Find the square root of 4096 using the factorization method.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"So, $$4096 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2}$$<br>\r\n$$\\\\sqrt{4096} = 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 = 64$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"32\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"So, $$4096 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2}$$<br>\r\n$$\\\\sqrt{4096} = 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 = 64$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"48\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"So, $$4096 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2}$$<br>\r\n$$\\\\sqrt{4096} = 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 = 64$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"72\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"So, $$4096 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2}$$<br>\r\n$$\\\\sqrt{4096} = 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 = 64$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"64\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"So, $$4096 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2}$$<br>\r\n$$\\\\sqrt{4096} = 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 = 64$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-1-1.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"So, $$4096 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2}$$<br>\r\n$$\\\\sqrt{4096} = 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 \\\\times 2 = 64$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-1-1.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the square root of 1000 using the long division method.\",\n                    \"text\": \"Find the square root of 1000 using the long division method.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Square root of 1000\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Square root of 1000\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100.66\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Square root of 1000\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"109.99\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Square root of 1000\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"31.622\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Square root of 1000 <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-2.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Square root of 1000 <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-2.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the square root of 2304 using the long division method.\",\n                    \"text\": \"Find the square root of 2304 using the long division method.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Square root of 2304\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"40\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Square root of 2304\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"42\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Square root of 2304\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Square root of 2304\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"48\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Square root of 2304 <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-3-1.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Square root of 2304 <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-3-1.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the least number by which 1800 must be multiplied to make it a perfect square.\",\n                    \"text\": \"Find the least number by which 1800 must be multiplied to make it a perfect square.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$1800 = 2 \u00d7 \\\\underline{2 \\\\times 2} \\\\times \\\\underline{5 \\\\times 5} \\\\times \\\\underline{3 \\\\times 3}$$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$$1800 \\\\times 2 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{5\\\\times5} \\\\times \\\\underline{3\\\\times3}$$<br>\r\n$$= 3600$$<br>\r\n$$\\\\sqrt{3600} = 2 \\\\times 2 \\\\times 5 \\\\times 3 = 60$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$1800 = 2 \u00d7 \\\\underline{2 \\\\times 2} \\\\times \\\\underline{5 \\\\times 5} \\\\times \\\\underline{3 \\\\times 3}$$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$$1800 \\\\times 2 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{5\\\\times5} \\\\times \\\\underline{3\\\\times3}$$<br>\r\n$$= 3600$$<br>\r\n$$\\\\sqrt{3600} = 2 \\\\times 2 \\\\times 5 \\\\times 3 = 60$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$1800 = 2 \u00d7 \\\\underline{2 \\\\times 2} \\\\times \\\\underline{5 \\\\times 5} \\\\times \\\\underline{3 \\\\times 3}$$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$$1800 \\\\times 2 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{5\\\\times5} \\\\times \\\\underline{3\\\\times3}$$<br>\r\n$$= 3600$$<br>\r\n$$\\\\sqrt{3600} = 2 \\\\times 2 \\\\times 5 \\\\times 3 = 60$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$1800 = 2 \u00d7 \\\\underline{2 \\\\times 2} \\\\times \\\\underline{5 \\\\times 5} \\\\times \\\\underline{3 \\\\times 3}$$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$$1800 \\\\times 2 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{5\\\\times5} \\\\times \\\\underline{3\\\\times3}$$<br>\r\n$$= 3600$$<br>\r\n$$\\\\sqrt{3600} = 2 \\\\times 2 \\\\times 5 \\\\times 3 = 60$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$1800 = 2 \u00d7 \\\\underline{2 \\\\times 2} \\\\times \\\\underline{5 \\\\times 5} \\\\times \\\\underline{3 \\\\times 3}$$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$$1800 \\\\times 2 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{5\\\\times5} \\\\times \\\\underline{3\\\\times3}$$<br>\r\n$$= 3600$$<br>\r\n$$\\\\sqrt{3600} = 2 \\\\times 2 \\\\times 5 \\\\times 3 = 60$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-4.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$1800 = 2 \u00d7 \\\\underline{2 \\\\times 2} \\\\times \\\\underline{5 \\\\times 5} \\\\times \\\\underline{3 \\\\times 3}$$<br>\r\nTo make a perfect square, there should be a pairing of factors.<br>\r\nHere, the first \u201c2\u201d has no pairing.<br>\r\nHence, we must multiply 1800 by 2 to make it a perfect square.<br>\r\n$$1800 \\\\times 2 = \\\\underline{2\\\\times2} \\\\times \\\\underline{2\\\\times2} \\\\times \\\\underline{5\\\\times5} \\\\times \\\\underline{3\\\\times3}$$<br>\r\n$$= 3600$$<br>\r\n$$\\\\sqrt{3600} = 2 \\\\times 2 \\\\times 5 \\\\times 3 = 60$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/12\/Practice-Problems-4.png\\\"\/>\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-500c3726-5d56-4aec-a997-ce0f61ca01c1\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-500c3726-5d56-4aec-a997-ce0f61ca01c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-500c3726-5d56-4aec-a997-ce0f61ca01c1\"><strong>What is the relationship between the Pythagorean theorem and square root<\/strong>?<\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-500c3726-5d56-4aec-a997-ce0f61ca01c1\">\n\n<p class=\"eplus-wrapper\">According to the Pythagorean theorem, the hypotenuse of a right-angled triangle is equal to the square root of the sum of its sides.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-500c3726-5d56-4aec-a997-ce0f61ca01c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-500c3726-5d56-4aec-a997-ce0f61ca01c1\"><strong>What is an example of an imperfect square?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-500c3726-5d56-4aec-a997-ce0f61ca01c1\">\n\n<p class=\"eplus-wrapper\">An imperfect square is a number whose square root is a fraction. An example is 50. \u221a50 = 7.07<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-500c3726-5d56-4aec-a997-ce0f61ca01c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-500c3726-5d56-4aec-a997-ce0f61ca01c1\"><strong>How are square and square roots related?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-500c3726-5d56-4aec-a997-ce0f61ca01c1\">\n\n<p class=\"eplus-wrapper\">Square and square roots are inverse operations. A square is a number obtained by multiplying the number by itself. On the other hand, the square root of a number is the number that, when multiplied by itself, gives the original number.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-500c3726-5d56-4aec-a997-ce0f61ca01c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-500c3726-5d56-4aec-a997-ce0f61ca01c1\"><strong>Can square roots be negative?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-500c3726-5d56-4aec-a997-ce0f61ca01c1\">\n\n<p class=\"eplus-wrapper\">Yes, every positive real number has two square roots\u2014positive and negative. For example, 5 and -5 are two square roots of 25. However, unless stated otherwise, the square root of a number refers to its positive square root (principal root). For example, the square root of 25 is 5.\u00a0<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-500c3726-5d56-4aec-a997-ce0f61ca01c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-500c3726-5d56-4aec-a997-ce0f61ca01c1\"><strong>Which method can be used to find the square root of a non-perfect square?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-500c3726-5d56-4aec-a997-ce0f61ca01c1\">\n\n<p class=\"eplus-wrapper\">We can use the long division method to find the square root of a non-perfect square. However, the factorization method can only be used for perfect squares.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Squares and Square Roots? When you multiply a number by itself, you get the square of a number. For instance, $3 \\times 3 = 9$. So, the square of 3 is 9. Square root goes the other way round. If the square of 3 is 9, then the square root of 9 is &#8230; <a title=\"Square and Square Roots\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots\" aria-label=\"More on Square and Square Roots\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-14274","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/14274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=14274"}],"version-history":[{"count":22,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/14274\/revisions"}],"predecessor-version":[{"id":42185,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/14274\/revisions\/42185"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=14274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=14274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=14274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}