{"id":26295,"date":"2023-03-14T06:09:00","date_gmt":"2023-03-14T06:09:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26295"},"modified":"2024-02-05T15:40:59","modified_gmt":"2024-02-05T15:40:59","slug":"perfect-squares-definition-formula-list-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares","title":{"rendered":"Perfect Squares &#8211; Definition, Formula, List, Examples"},"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-1db19781-1f5e-4734-b78c-fe5907d10791\" 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\/perfect-squares#0-what-are-perfect-squares>What Are Perfect Squares?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares#7-perfect-squares-list>Perfect Squares List<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares#8-how-to-identify-perfect-squares>How to Identify Perfect Squares<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares#13-solved-examples-on-perfect-squares>Solved Examples on Perfect Squares<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares#14-practice-problems-on-perfect-squares>Practice Problems on Perfect Squares<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares#15-frequently-asked-questions-on-perfect-squares>Frequently Asked Questions on Perfect Squares<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-perfect-squares\">What Are Perfect Squares?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>A number expressed as a product of an integer by itself is called a perfect square<\/strong>. Since the same number is multiplied twice, the perfect square is also written as the second exponent of an integer. Thus, the squares of all integers are known as perfect squares.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example<\/strong>: 16 is a perfect square since it is a product of an integer with itself.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4 \\times 4 = 16$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, the product $(-\\;4)$ with $(-\\;4)$ gives 16.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(-\\;4) \\times (-\\;4) = 16$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Notice that the squares of 4 and $-4$ are the same.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-perfect-squares-definition\">Perfect Squares: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The definition of perfect squares in math can be given as the positive integers obtained by multiplying an integer with itself.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find a perfect square, simply multiply any integer by itself!<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">How to denote a perfect square? We write \u201c2\u201d as the power of the given number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We read $5^2$ as \u201cfive squared.\u201d<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"404\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/five-squared-equals-twentyfive.webp\" alt=\"5 squared equals 25\" class=\"wp-image-33128\" title=\"5 squared equals 25\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/five-squared-equals-twentyfive.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/five-squared-equals-twentyfive-300x195.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\/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\/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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-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_1_pt.png\" alt=\"Identify 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\">Identify 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\/identify-the-perimeter-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_peri_unit_square_2_pt.png\" alt=\"Identify the Perimeter 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\">Identify the Perimeter 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\/identify-triangles-and-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\/geometry_triangles_squares_pt.png\" alt=\"Identify Triangles and 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\">Identify Triangles and 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\/match-triangles-and-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\/geometry_amusement_park_4_5_gm.png\" alt=\"Match Triangles and 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\">Match Triangles and 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\/order-objects-by-counting-the-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\/measurement_order_by_counting_squares_pt.png\" alt=\"Order Objects by Counting the 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\">Order Objects by Counting the 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><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=\"2-examples-of-perfect-squares\">Examples of Perfect Squares<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here are a few examples of perfect squares.<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$1^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$2^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>4&nbsp;<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$3^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>9&nbsp;<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$4^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>16<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$5^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>25&nbsp;<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$6^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>36&nbsp;<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$7^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>49&nbsp;<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$8^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>64<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$9^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>81&nbsp;<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$10^2 =$<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>100&nbsp;<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s consider the visual representation. Perfect squares can be represented in the shape of a square. In other words, you can represent them in equal numbers of rows and columns in a multiplication array.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: <\/strong>Suppose you have 4 marbles. You can arrange them in 2 rows and 2 columns such that they will fit in a square shape. Similarly, you can arrange 9 marbles in a square shape using 3 rows and 3 columns.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"629\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-perfect-squares-by-fitting-marbles-in-square-shapes.png\" alt=\"Visualizing perfect squares by fitting marbles in square shapes\" class=\"wp-image-33130\" title=\"Visualizing perfect squares by fitting marbles in square shapes\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-perfect-squares-by-fitting-marbles-in-square-shapes.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-perfect-squares-by-fitting-marbles-in-square-shapes-296x300.png 296w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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=\"3-non-examples-of-perfect-squares\">Non Examples of Perfect Squares<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If you take 6 marbles, you can either arrange them in an array of 2 rows and 3 columns, or 3 rows and 2 columns. Now that the number of rows and columns are different, the number 6 cannot be a perfect square number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualize-non-examples-of-perfect-squares-using-an-array.png\" alt=\"Visualize non-examples of perfect squares using an array\" class=\"wp-image-33131\" title=\"Visualize non-examples of perfect squares using an array\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualize-non-examples-of-perfect-squares-using-an-array.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualize-non-examples-of-perfect-squares-using-an-array-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-perfect-squares-formula\">Perfect Squares: Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since perfect squares are numbers that can be expressed as a product of an integer with itself which ultimately gives us the square of that integer. The perfect squares formula can be expressed as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$P = n \\times n = n^2$<sup> <\/sup>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where P denotes a perfect square number and n denotes an integer.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-perfect-square-numbers\">Perfect Square Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Perfect square numbers are positive integers that correspond to the multiplication of two of the same integers with themselves<\/strong>. It can also be that if you take the root of a perfect square number, you will only get a whole number. Below is a perfect squares list of the first 100 natural numbers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-perfect-squares-chart-from-1-to-100\">Perfect Squares Chart (From 1 to 100)<\/h2>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>&nbsp; &nbsp; &nbsp; &nbsp; Perfect Squares from 1 to 100<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">                                       <\/td><td class=\"has-text-align-center\" data-align=\"center\">                                    <\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$1 \\times 1$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$1^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$2 \\times 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$2^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$3 \\times 3$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$3^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$4 \\times 4$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$4^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">16<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$5 \\times 5$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$5^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">25<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$6 \\times 6$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$6^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">36<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$7 \\times 7$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$7^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">49<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$8 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$8^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">64<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$9 \\times 9$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$9^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">81<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$10 \\times 10$<\/td><td class=\"has-text-align-center\" data-align=\"center\">$10^2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">100<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-perfect-squares-list\">Perfect Squares List<\/h2>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td>$1^2 = 1$<\/td><td>$2^2 = 4$<\/td><td>$3^2 = 9$<\/td><td>$4^2 = 16$<\/td><td>$5^2 = 25$<\/td><td>$6^2 = 36$<\/td><td>$7^2 = 49$<\/td><td>$8^2 = 64$<\/td><td>$9^2 =81$&nbsp;<\/td><td>$10^2 = 100$<\/td><\/tr><tr><td>$11^2 = 121$<\/td><td>$12^2 = 144$<\/td><td>$13^2 = 169$<\/td><td>$14^2 = 196$<\/td><td>$15^2 = 225$<\/td><td>$16^2 = 256$<\/td><td>$17^2 = 289$<\/td><td>$18^2 = 324$<\/td><td>$19^2 = 361$<\/td><td>$20^2 = 400$<\/td><\/tr><tr><td>$21^2 = 441$<\/td><td>$22^2 = 484$<\/td><td>$23^2 = 529$<\/td><td>$24^2 = 576$<\/td><td>$25^2 = 625$<\/td><td>$26^2 = 676$<\/td><td>$27^2 = 729$<\/td><td>$28^2 = 784$<\/td><td>$29^2 = 841$<\/td><td>$30^2 = 900$<\/td><\/tr><tr><td>$31^2 = 961$<\/td><td>$32^2 = 1024$<\/td><td>$33^2 = 1089$<\/td><td>$34^2 = 1156$<\/td><td>$35^2 = 1225$<\/td><td>$36^2 = 1296$<\/td><td>$37^2<br>= 1369$<\/td><td>$38^2 = 1444$<\/td><td>$39<sup>^2<\/sup> = 1521$<\/td><td>$40^2 = 1600$<\/td><\/tr><tr><td>$41^2 = 1681$<\/td><td>$42^2 = 1764$<\/td><td>$43^2 = 1849$<\/td><td>$44^2 = 1836$<\/td><td>$45^2 = 2025$<\/td><td>$46^2 = 2116$<\/td><td>$47^2 = 2209$<\/td><td>$48^2 = 2304$<\/td><td>$49^2 = 2401$<\/td><td>$50^2 = 2500$<\/td><\/tr><tr><td>$51^2 = 2601$<\/td><td>$52^2 = 2704$<\/td><td>$53^2 = 2809$<\/td><td>$54^2 = 2916$<\/td><td>$55^2 = 3025$<\/td><td>$56^2 = 3136$<\/td><td>$57^2 = 3249$<\/td><td>$58^2 = 3364$<\/td><td>$59^2 = 3481$<\/td><td>$60^2 = 3600$<\/td><\/tr><tr><td>$61^2 = 3721$<\/td><td>$62^2 = 3844$<\/td><td>$63^2 = 3969$<\/td><td>$64^2 = 4096$<\/td><td>$65^2 = 4225$<\/td><td>$66^2 = 4356$<\/td><td>$67^2 = 4489$<\/td><td>$68^2 = 4624$<\/td><td>$69^2 = 4761$<\/td><td>$70^2 = 4900$<\/td><\/tr><tr><td>$71^2 = 5041$<\/td><td>$72^2 = 5184$<\/td><td>$73^2 = 5329$<\/td><td>$74^2 = 5476$<\/td><td>$75^2 = 5625$<\/td><td>$76^2 = 5776$<\/td><td>$77^2 = 5929$<\/td><td>$78^2 = 6084$<\/td><td>$79^2 = 6241$<\/td><td>$80^2 = 6400$<\/td><\/tr><tr><td>$81^2 = 6561$<\/td><td>$82^2 = 6724$<\/td><td>$83^2 = 6889$<\/td><td>$84^2 = 7056$<\/td><td>$85^2 = 7225$<\/td><td>$86^2 = 7396$<\/td><td>$87^2 = 7569$<\/td><td>$88^2 = 7744$<\/td><td>$89^2 = 7921$<\/td><td>$90^2 = 8100$<\/td><\/tr><tr><td>$91^2 = 8281$<\/td><td>$92^2 = 8464$<\/td><td>$93^2 = 8649$<\/td><td>$94^2 = 8836$<\/td><td>$95^2 = 9025$<\/td><td>$96^2 = 9216$<\/td><td>$97^2 = 9409$<\/td><td>$98^2 = 9604$<\/td><td>$99^2 = 9801$<\/td><td>$100^2 = 10000$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-how-to-identify-perfect-squares\">How to Identify Perfect Squares<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To identify perfect squares, we mostly have to pay attention to the last digit of the number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the chart, we see that the integers 1, 2, 7, 8 never appear at the ones place. The ones place has the numbers 0, 1, 4, 5, 6, or 9.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can deduce that numbers with 00, 1, 4, 5, 6, 9 as their last digit <strong>can be<\/strong> perfect squares. So, if the last digit is 2, 3, 7, or 8, the given number is not a perfect square.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here are some other observations you can make!<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Perfect squares of numbers ending with 3 or 7 have 9 at their ones place.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Perfect squares of numbers ending with 5 have 5 at their ones place.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Perfect squares of numbers ending with 4 or 6 have 6 at their ones place.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Perfect squares of numbers ending with 2 or 8 have 4 at their ones place.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Perfect squares of numbers ending with 1 and 9 have 1 at their ones place.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In summary, here are some \u2018perfect square rules\u2019 or tests you can apply to identify a perfect square.<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">All perfect squares end in 1, 4, 5, 6, 9 or 00 (even number of zeros). Thus, a number that ends in 2, 3, 7 or 8 is not a perfect square.<\/li>\n<\/ol>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">No number can be a perfect square unless its digital root is 1, 4, 7, or 9.<\/li>\n<\/ol>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Total numbers of prime factors of a perfect square are always odd.<\/li>\n<\/ol>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If the unit digit ends in 5, tens digit is always 2.<\/li>\n<\/ol>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If a number ends with zero, you may look at how many zeroes are at the end. If the number of zeroes is odd, the number isn&#8217;t a perfect square. If the number of zeroes is even, then it <strong>might be<\/strong> a perfect square.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, 1000 has an odd number of zeroes, so it is not a perfect square number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$400 = 20^2$ \u2026 a perfect square<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">300 \u2026 not a perfect square<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-identify-perfect-squares-using-the-square-root\">Identify Perfect Squares Using the Square Root<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">One other way to check if a number is a perfect square is by finding out the square root of the number. The integer that is multiplied with itself to find the perfect square is called the \u201csquare root\u201d of the perfect square.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, 4 and $-4$ are square roots of 16.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If the square root comes out to be an integer, then the given number is a perfect square.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If the square root comes out to be a decimal number, then the given number is not a perfect square number.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1: <\/strong>$\\sqrt{24} = 4.89$, which is not an integer. Thus, 24 is not a perfect square.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2: <\/strong>$\\sqrt{49} = \\pm\\; 7$, which is an integer. Thus, 49 is a perfect square.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-tips-and-tricks-to-find-perfect-squares\">Tips and Tricks to Find Perfect Squares<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Sometimes, we can find perfect squares of some numbers without using the long multiplication method.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1:<\/strong> Numbers ending with the digit 5<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Separate the two digits of the number. Take the tens place digit and multiply it by its successor. Square the unit place digit. Write these two results together. $75^2 = 5625$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/perfect-square-tips-and-tricks.png\" alt=\"Perfect square tips and tricks\" class=\"wp-image-33132\" title=\"Perfect square tips and tricks\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/perfect-square-tips-and-tricks.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/perfect-square-tips-and-tricks-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2:<\/strong> Using the formula $(a + b)^2 = a^2 + 2ab + b^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the square of large numbers, you can split them into friendly numbers using the above formula and then expand.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$67^2 = (60 + 7)^2 = 60^2 + 2(60)(7) + 7^2$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 3600 + 840 + 49$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong><em>&nbsp;&nbsp;&nbsp;&nbsp;<\/em><\/strong>$= 4489$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-facts-about-perfect-squares\">Facts about Perfect Squares<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If a number has zero at the ones place, then the square of the number will always have even numbers of zeros at the end.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Square roots of negative numbers are undefined. There doesn\u2019t exist any negative perfect square numbers.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The area of the geometric shape \u201csquare\u201d having side \u201cs\u201d is given by $s \\times s = s^2$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The principal square root of a number is the positive square root. Usually, \u201cthe square root\u201d of a number refers only to the principal square root or the positive root.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we discussed the concept of perfect squares and learned how to identify them. We also discussed the definition of a perfect square, formula to find the perfect square. Let\u2019s solve a few examples for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-solved-examples-on-perfect-squares\">Solved Examples on Perfect Squares<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Find the perfect square of 13 using the formula <\/strong>$(a + b)^2 = a^2 + 2ab + b^2$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We will split 13 as $(10 + 3)$ to use the formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$13 \\times 13 = 13^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= (10 + 3)^2\\;                                     \u2026(a+b)^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 100 + 60 + 9\\;                                 \u2026(a + b)^2 = a^2 + 2ab + b^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 169$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. <\/strong><strong>Determine if 3600 is a perfect square or not.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since 3600 ends with two zeros, it is likely that 3600 is a perfect square number. Factoring 3600 gives us the following expression:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3600 = 6 \\times 6 \\times 10 \\times 10 = 60 \\times 60$, which satisfies the condition of perfect square numbers. So, 3600 is a perfect square number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. <\/strong><strong>What is the smallest whole number to be added to 55 to make it a perfect square?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The next closest perfect square number to 55 is 64, which is the perfect square of 8.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$64\\;-\\;55 = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we add 9 to 55, we will get 64, which is a perfect square number.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-practice-problems-on-perfect-squares\">Practice Problems on Perfect Squares<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Perfect Squares - Definition, Formula, List, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Identify the perfect square.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">125<\/div><div class=\"spq_answer_block\" data-value=\"1\">225<\/div><div class=\"spq_answer_block\" data-value=\"2\">325<\/div><div class=\"spq_answer_block\" data-value=\"3\"> 525<\/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: 225<br\/>225 is a perfect square since $15 \\times 15 = 225$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find the positive square root of 9.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3<\/div><div class=\"spq_answer_block\" data-value=\"1\">-3<\/div><div class=\"spq_answer_block\" data-value=\"2\">9<\/div><div class=\"spq_answer_block\" data-value=\"3\">Both a and b<\/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: 3<br\/>$3 \\times 3 = 3^2 = 9$<\/span><\/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\">$85^2 =$ ____<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5625<\/div><div class=\"spq_answer_block\" data-value=\"1\">8825<\/div><div class=\"spq_answer_block\" data-value=\"2\">7225<\/div><div class=\"spq_answer_block\" data-value=\"3\">5625<\/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: 7225<br\/>Use the trick. Split the number as 8-5.<br>\r\n$8 \\times 9 = 9\\;$\t\t\u2026multiply 8 with its successor<br>\r\n$5^2 = 25$<br>\r\nThus, $85^2 = 7225$<\/span><\/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\": \"Perfect Squares - Definition, Formula, List, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Perfect Squares\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the perfect square.\",\n                    \"text\": \"Identify the perfect square.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"225 is a perfect square since $$15 \\\\times 15 = 225$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"125\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"225 is a perfect square since $$15 \\\\times 15 = 225$$.\"\n                                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225$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"225\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"225 is a perfect square since $$15 \\\\times 15 = 225$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"225 is a perfect square since $$15 \\\\times 15 = 225$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the positive square root of 9.\",\n                    \"text\": \"Find the positive square root of 9.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$3 \\\\times 3 = 3^2 = 9$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"-3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3 \\\\times 3 = 3^2 = 9$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n     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Split the number as 8-5.<br>\r\n$$8 \\\\times 9 = 9\\\\;$$\t\t\u2026multiply 8 with its successor<br>\r\n$$5^2 = 25$$<br>\r\nThus, $$85^2 = 7225$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5625\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Use the trick. Split the number as 8-5.<br>\r\n$$8 \\\\times 9 = 9\\\\;$$\t\t\u2026multiply 8 with its successor<br>\r\n$$5^2 = 25$$<br>\r\nThus, $$85^2 = 7225$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8825\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Use the trick. Split the number as 8-5.<br>\r\n$$8 \\\\times 9 = 9\\\\;$$\t\t\u2026multiply 8 with its successor<br>\r\n$$5^2 = 25$$<br>\r\nThus, $$85^2 = 7225$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5625\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Use the trick. Split the number as 8-5.<br>\r\n$$8 \\\\times 9 = 9\\\\;$$\t\t\u2026multiply 8 with its successor<br>\r\n$$5^2 = 25$$<br>\r\nThus, $$85^2 = 7225$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7225\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Use the trick. Split the number as 8-5.<br>\r\n$$8 \\\\times 9 = 9\\\\;$$\t\t\u2026multiply 8 with its successor<br>\r\n$$5^2 = 25$$<br>\r\nThus, $$85^2 = 7225$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Use the trick. Split the number as 8-5.<br>\r\n$$8 \\\\times 9 = 9\\\\;$$\t\t\u2026multiply 8 with its successor<br>\r\n$$5^2 = 25$$<br>\r\nThus, $$85^2 = 7225$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-frequently-asked-questions-on-perfect-squares\">Frequently Asked Questions on Perfect Squares<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-e00be29b-00d7-437b-a3e1-9a70893a4e12\" 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-e00be29b-00d7-437b-a3e1-9a70893a4e12\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e00be29b-00d7-437b-a3e1-9a70893a4e12\"><strong>How many perfect square numbers are there between 1 and 100?<\/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-e00be29b-00d7-437b-a3e1-9a70893a4e12\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are 10 perfect square numbers between 1 and 100.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">1, 4, 9, 16, 25, 36, 49, 64, 81, and 100<\/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-e00be29b-00d7-437b-a3e1-9a70893a4e12\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e00be29b-00d7-437b-a3e1-9a70893a4e12\"><strong>What are perfect cubes?<\/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-e00be29b-00d7-437b-a3e1-9a70893a4e12\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perfect cubes are numbers that are obtained by multiplying an integer with itself three times. For example, 27 is a perfect cube of the integer 3.<\/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-e00be29b-00d7-437b-a3e1-9a70893a4e12\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e00be29b-00d7-437b-a3e1-9a70893a4e12\"><strong>Is -25 a perfect square number?<\/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-e00be29b-00d7-437b-a3e1-9a70893a4e12\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">-25 is not a perfect square number. The product of a number with itself cannot be negative.<\/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-e00be29b-00d7-437b-a3e1-9a70893a4e12\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e00be29b-00d7-437b-a3e1-9a70893a4e12\"><strong>Is 5 a 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-3-e00be29b-00d7-437b-a3e1-9a70893a4e12\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">5 is not a perfect square.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Perfect Squares? A number expressed as a product of an integer by itself is called a perfect square. Since the same number is multiplied twice, the perfect square is also written as the second exponent of an integer. Thus, the squares of all integers are known as perfect squares. Example: 16 is a &#8230; <a title=\"Perfect Squares &#8211; Definition, Formula, List, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/perfect-squares\" aria-label=\"More on Perfect Squares &#8211; Definition, Formula, List, Examples\">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-26295","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\/26295","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=26295"}],"version-history":[{"count":21,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26295\/revisions"}],"predecessor-version":[{"id":39948,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26295\/revisions\/39948"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}