{"id":27019,"date":"2023-03-31T19:30:05","date_gmt":"2023-03-31T19:30:05","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27019"},"modified":"2024-02-05T15:29:44","modified_gmt":"2024-02-05T15:29:44","slug":"solving-radical-equations-steps-definition-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving","title":{"rendered":"Solving Radical Equations: Steps, Definition, 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-bf64ec9a-793c-4ba3-91ce-4dcb349a0b69\" 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\/radical-equations-solving#0-what-are-radical-equations>What Are Radical Equations?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving#1-radical-equations-definition>Radical Equations Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving#2-how-to-solve-radical-equations>How to Solve Radical Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving#7-solved-examples-on-radical-equations>Solved Examples on Radical Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving#8-practice-problems-on-radical-equations>Practice Problems on Radical Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving#9-frequently-asked-questions-about-radical-equations>Frequently Asked Questions about Radical Equations<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-radical-equations\">What Are Radical Equations?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Radical equations are equations in which a variable is under a radical symbol.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Before we explore the concept of radical equations, let\u2019s quickly take a look at the important terminologies that will be helpful.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Radical symbol: <\/strong>The symbol \u201c\u23b7\u201d that we use to denote square root, cube root, or nth root (like $\\sqrt{},\\; ^3\\sqrt{},\\; ^4\\sqrt{}$, etc.) is called a \u201cradical symbol.\u201d&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The horizontal line at the top is called the vinculum.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In the radical symbol, $(\\sqrt{}$ or $^2\\sqrt{}),\\; ^3\\sqrt{},\\; ^4\\sqrt{}$, etc., the numbers 2, 3, and 4 written in the little dent represent the \u201cindex.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the index is not written, it is considered to be 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Radical expression:<\/strong> A radical expression is the expression that has an n<sup>th<\/sup> root (usually a square root).<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Radicand:<\/strong> A number or expression inside the radical symbol.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"273\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/parts-of-radicals.png\" alt=\"Parts of radicals\" class=\"wp-image-34634\" title=\"Parts of radicals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/parts-of-radicals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/parts-of-radicals-300x132.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Important Note:<\/strong> The square root of a number in an exponent form is the number raised to the power of $\\frac{1}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{x} = x^\\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The n<sup>th<\/sup> root of x can be written as $^n\\sqrt{x} = x^\\frac{1}{n}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The n<sup>th<\/sup> root of xm can be written as $^n\\sqrt{x}^m = x^\\frac{m}{n}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Examples:<\/strong> $^3\\sqrt{x^2} = (x^2)\\frac{1}{3} = x^\\frac{2}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$^3\\sqrt{x^4} = x^\\frac{4}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$^2\\sqrt{x^5} = x^\\frac{5}{2}$ etc.<\/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\/find-the-missing-number-in-addition-equations\" 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\/add_sub_pv_add_3d_2d_missing_pt.png\" alt=\"Find the Missing Number in Addition Equations 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 Missing Number in Addition Equations 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 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src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_sub_3d_2d_match_pt.png\" alt=\"Subtract 2-Digit Numbers to Complete the Equations 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\">Subtract 2-Digit Numbers to Complete the Equations 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\/subtract-3-digit-numbers-to-complete-the-equations\" 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\/add_sub_pv_sub_3d_3d_match_pt.png\" alt=\"Subtract 3-Digit Numbers to Complete the Equations 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\">Subtract 3-Digit Numbers to Complete the Equations 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\/subtraction-equations\" 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\/add_sub_facts_sub_sent_w5_pt.png\" alt=\"Subtraction Equations 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\">Subtraction Equations 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\/use-subtraction-to-complete-the-equations\" 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\/add_sub_pv_sub_3d_1d_match_pt.png\" alt=\"Use Subtraction to Complete the Equations 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\">Use Subtraction to Complete the Equations 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 = 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}\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-radical-equations-definition\">Radical Equations Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A radical equation is an equation in which a variable is in the radicand of the expression.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">At least one radical sign of a radical equation includes a variable.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In other words, a radical equation has a variable with a rational exponent.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Examples of Radical Equations:<\/strong> $\\sqrt{a} + 4 = 13,\\; \\sqrt{x\\;-\\;1} = 5$&nbsp;<\/p>\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\/complete-the-addition-equations\" 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\/complete-the-addition-equations.jpeg\" alt=\"Complete the Addition Equations 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-equations-using-distributive-property\" 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\/complete-the-equations-using-distributive-property.jpeg\" alt=\"Complete the Equations using Distributive Property 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-equations\" data-vars-ga-category=\"splashlearn_vocab\" 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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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/represent-and-solve-subtraction-equations\" 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\/represent-and-solve-subtraction-equations.jpeg\" alt=\"Represent and Solve Subtraction Equations 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/represent-the-arrays-using-equations\" 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});\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-solve-radical-equations\">How to Solve Radical Equations<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Solving a radical equation simply means finding the value of the variable. The variable in a radical equation is under the radical sign. Thus, exponent rules and fundamental algebraic principles must be followed in order to solve radical equations. A square root can be eliminated by squaring, and cube roots can be eliminated by cubing, etc.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note that the solutions obtained by solving a radical equation must be verified.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The binomial square formulas are extremely useful when solving a radical equation where a binomial term is present on one side of the radical equation.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$(a + b)^2 = a^2 + 2ab + b^2$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$(a\\;-\\;b)^2 = a^2\\;-\\;2ab + b^2$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s discuss the steps to solving radical equations with two cases.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">I. Solving Radical Equation With One Radical<\/p>\n\n\n\n<p class=\"eplus-wrapper\">II. Solving Radical Equations with Two Radicals&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-solving-radical-equation-with-one-radical\">Solving Radical Equation with One Radical<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Isolate the radical symbol on one side of the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>Eliminate the radical symbol by raising both sides of the equation to the power of the index. If it is a square root, then square both sides; if it is a cube root, cube both sides; and so on.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>Solve the obtained equation using the following formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For $x \\gt 0$, we have $(^n\\sqrt{x})^n = x$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: <\/strong>Verify by substituting the answer in the original equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong><em>(Note:<\/em><\/strong><em> The principal square root of a number can only be positive. A radical sign indicates a positive root. So, an equation will not have a solution if its radical has an even index equal to a negative number.)<\/em><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Solve <\/strong>$\\sqrt{2x + 3} \\;-\\; 5 = 0$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Isolate the radical symbol.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Add 5 on both sides. Use the <strong>addition property of equality<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{2x + 3} = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>Eliminate the radical symbol.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To eliminate the radicals, square both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\sqrt{2x + 3})^2 = 5^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 2x + 3 = 25$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>Solve the obtained equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x = 25\\;-\\;3 = 22$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x = \\frac{22}{2} = 11$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: <\/strong>Verify the answer.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substitute $x = 11$ in the given equation, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= \\sqrt{2 \\times 11 + 3} \\;-\\; 5 = \\sqrt{25} \\;-\\; 5 = 5 \\;-\\; 5 = 0 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $x = 11$ is the solution of the given equation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-solving-radical-equations-with-two-radicals\">Solving Radical Equations with Two Radicals<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">If there are two in the radical equation, we begin by isolating one of the two radicals. Isolating the more complicated radical first often works best.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: <\/strong>Isolate one of the radical terms on one side of the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>Eliminate the radicals by raising both sides of the equation to the power of the index. This means that if it is a square root, then square both sides; if it is a cube root, cube both sides; etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>Solve the obtained equation once the radical signs are eliminated.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/steps-for-solving-radical-equations-with-two-radicals.png\" alt=\"Steps for solving radical equations with two radicals\" class=\"wp-image-34635\" title=\"Steps for solving radical equations with two radicals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/steps-for-solving-radical-equations-with-two-radicals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/steps-for-solving-radical-equations-with-two-radicals-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: <\/strong>Verify the answer in the original equation and check whether it is satisfying or not.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let&#8217;s use this concept to solve an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Solve <\/strong>$\\sqrt{x + 5} \\;-\\; \\sqrt{x} = 2$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: <\/strong>Isolate one of the radical terms on one side of the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{x + 5} = 2 + \\sqrt{x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>Eliminate the radicals.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To eliminate the radicals, square both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\sqrt{x+5})^2 = (2 + \\sqrt{x})^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x + 5 = 4 + 4 \\sqrt{x} + x$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>Solve the obtained equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 1 = 4 \\sqrt{x}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since a radical is still present in the obtained equation, square both sides again.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1 = 16x$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = \\frac{1}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: <\/strong>Verify the answer.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substitute x=116 in the given equation, and we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $\\sqrt{\\frac{1}{16} + 5} \\;-\\; \\sqrt{\\frac{1}{16}} = \\sqrt{\\frac{81}{16}}\\;-\\; \\sqrt{\\frac{1}{16}} = \\frac{9}{4}\\;-\\; \\frac{1}{4}=2 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $x = \\frac{1}{16}$ is the solution of the given equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Note:<\/strong> A quadratic equation of the form $ax^2 + bx + c = 0$ obtained in the process of solving a radical equation can also be solved using the <strong>quadratic formula<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"292\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/quadratic-formula.png\" alt=\"Quadratic formula\" class=\"wp-image-34637\" title=\"Quadratic formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/quadratic-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/quadratic-formula-300x141.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-facts-about-radical-equations\">Facts about Radical Equations<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The modern radical sign, &#8220;\u221a&#8221; was first introduced by a German mathematician Christoff Rudolff.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">European paper sizes are a good illustration of how a radical is used in the real world. The measurements of an A4-sized sheet of paper are $8.27 \\times 11.67$ inches. The ratio of the lengths of the longer and shorter side of an A4 paper is approximately $\\sqrt{2}$.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When you square a radical equation, you sometimes get solutions to the squared equation which may not satisfy the original equation. Such a solution is called an <strong>extraneous solution<\/strong>. Thus, if you raise both sides of an equation by some power, then you have to verify your solutions to eliminate the extraneous solutions.&nbsp;<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we have discussed the radicals, methods, and steps for solving radical equations. Let\u2019s solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-radical-equations\">Solved Examples on Radical Equations<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Solve <\/strong>$\\sqrt{3x^2\\;-\\;12x} = 6$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, $\\sqrt{3x^2\\;-\\;12x} =6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To eliminate the radical sign, square both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\bigg(\\sqrt{3x^2\\;-\\;12x}\\bigg)^2 = 6^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 3x^2\\;-\\;12x = 36$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 3x^2\\;-\\;12x\\;-\\;36 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 3(x^2\\;-\\;4x\\;-\\;12) = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x^2\\;-\\;4x\\;-\\;12 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x^2\\;-\\;6x + 2x\\;-\\;12 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x(x\\;-\\;6) + 2(x\\;-\\;6) = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow (x + 2) (x\\;-\\;6)=0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x=\\;-\\;2,\\; 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Verification:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For $x = \\;-2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $\\sqrt{3(\\;-\\;2)^2\\;-\\;12(\\;-\\;2)} = \\sqrt{12+24} = \\sqrt{36} = 6 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For $x = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= \\sqrt{3(6)^2\\;-\\;12(6)} = \\sqrt{108\\;-\\;72} = \\sqrt{36} = 6 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the solution of the given equation is $x = \\;-\\;2,\\; 6$.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Solve:&nbsp; <\/strong>$^3sqrt{x\\;-\\;1} = 3$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$^3\\sqrt{x\\;-\\;1} = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To eliminate the radical, cube both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(^3\\sqrt{x\\;-\\;1})^3 = 3^3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x\\;-\\;1 = 27$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 28$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Verification:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For $x = 28$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= ^3\\sqrt{x\\;-\\;1} = ^3\\sqrt{28\\;-\\;1} = ^3\\sqrt{27} = 3 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the solution of the given equation is $x = 28$.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Solve <\/strong>$^3\\sqrt{2x + 4} + 8 = 4$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, $^3\\sqrt{2x + 4} + 8 = \\;-4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the radical is not isolated, so first isolate the radical on one side.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$^3\\sqrt{2x + 4} =\\; -4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To eliminate the radicals, cube both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(^3\\sqrt{2x+4})^3 =(-4)^3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 2x + 4 =\\; -64$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 2x = \\;-64\\;-\\;4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 2x= \\;-68$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x = \\frac{-68}{2} =\\; -34$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Verification:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For $x = \\;-34$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= ^3\\sqrt{2(\\;-\\;34)+4} + 8 = ^3\\sqrt{\\;-\\;68+4} + 8 = ^3\\sqrt{\\;-\\;64} + 8= \\;-4 + 8 = 4 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the solution of the given equation is $x = \\;-34$.<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Solve <\/strong>$\\sqrt{x\\;-\\;2} + \\sqrt{x\\;-\\;1} = 1$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, $\\sqrt{x\\;-\\;2} + \\sqrt{x\\;-\\;1} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the radical is not isolated, so first isolate the radical on one side.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{x \\;-\\; 2} = 1\\;-\\; \\sqrt{x\\;-\\;1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To eliminate the radicals, square both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\sqrt{x-2})^2 = (1-\\sqrt{x\\;-\\;1})^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x\\;-\\;2 = 1\\;-\\;2 \\sqrt{x\\;-\\;1} + x\\;-\\;1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow \\;-\\;2 = \\;-\\;2\\sqrt{x\\;-\\;1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 1 = \\sqrt{x\\;-\\;1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Squaring both sides again, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1 = x\\;-\\;1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Verification:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For $x = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= \\sqrt{x\\;-\\;2} + \\sqrt{x\\;-\\;1} = \\sqrt{2\\;-\\;2} + \\sqrt{2\\;-\\;1} = 0 + 1 = 1 =$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the solution of the given equation is $x = 2$.<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\sqrt{x + 4} =x \\;-\\; 2$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$sqrt{x + 4} = x &#8211; 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Squaring both sides:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x + 4 = (x\\;-\\;2)^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x + 4 = x^2\\;-\\;4x + 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x^2\\;-\\;5x = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x (x\\;-\\;5) = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 0 ; x = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Verification:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Put $x = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= \\sqrt{0+4}  = \\sqrt{4} = 2$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">R.H.S. $= 0 \\;-\\; 2&nbsp;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $\\neq$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $x = 0$ is not the solution.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Put $x = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $= \\sqrt{5 + 4} = \\sqrt{9} = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">R.H.S. $= 5\\;-\\;2 = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L.H.S. $=$ R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $x = 5$ is the solution.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-radical-equations\">Practice Problems on Radical Equations<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Solving Radical Equations: Steps, Definition, Examples<\/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\">The radicand of the expression $7^3\\sqrt{9}$ is equal to____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$7$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$7^3\\sqrt{9}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$9$<\/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: $9$<br\/>The number inside the radical sign is called the radicand of the number. Hence, in  $^3\\sqrt{9}$, the radicand is 9.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The index of the radical number $^5\\sqrt{4^3}$ is equal to____.<\/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: 5<br\/>In the given number $^5\\sqrt{4^3}$,  the index of the radical is 5.<\/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\">Solve the radical equation: $\\sqrt{x }\\;-\\;1 = 2$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">9<\/div><div class=\"spq_answer_block\" data-value=\"3\">3<\/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: 9<br\/>$\\sqrt{x} \\;-\\;1 = 2$<br>\r\n$\\sqrt{x} = 3$\t\t\u2026isolate the radical<br>\r\n$x = 9$\t\t\t\u2026square both sides<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the value of \u201cx\u201d in the radical equation $\\sqrt{2x} = 4$ ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">4<\/div><div class=\"spq_answer_block\" data-value=\"2\">8<\/div><div class=\"spq_answer_block\" data-value=\"3\">12<\/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: 8<br\/>Given: the radical equation $\\sqrt{2x} = 4$.<br>\r\nSquaring both sides, we get $2x = 16 \\Rightarrow x = 8$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the value of \u201cm\u201d in the radical equation  $^3\\sqrt{m} = 3$ ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3<\/div><div class=\"spq_answer_block\" data-value=\"1\">9<\/div><div class=\"spq_answer_block\" data-value=\"2\">27<\/div><div class=\"spq_answer_block\" data-value=\"3\">81<\/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: 27<br\/>Given: the radical equation  $^3\\sqrt{m} = 3$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$m = 3^3 = 27$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">The equation $\\sqrt{a\\;-\\;1} = \\;-3$ has<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">One solution<\/div><div class=\"spq_answer_block\" data-value=\"1\">No solution<\/div><div class=\"spq_answer_block\" data-value=\"2\">many solutions<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: No solution<br\/>The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $\u22123$.<\/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\": \"Solving Radical Equations: Steps, Definition, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Solving Radical Equations\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The radicand of the expression $$7^3\\\\sqrt{9}$$ is equal to____.\",\n                    \"text\": \"The radicand of the expression $$7^3\\\\sqrt{9}$$ is equal to____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The number inside the radical sign is called the radicand of the number. Hence, in  $$^3\\\\sqrt{9}$$, the radicand is 9.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number inside the radical sign is called the radicand of the number. Hence, in  $$^3\\\\sqrt{9}$$, the radicand is 9.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number inside the radical sign is called the radicand of the number. Hence, in  $$^3\\\\sqrt{9}$$, the radicand is 9.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7^3\\\\sqrt{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number inside the radical sign is called the radicand of the number. Hence, in  $$^3\\\\sqrt{9}$$, the radicand is 9.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$9$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The number inside the radical sign is called the radicand of the number. Hence, in  $$^3\\\\sqrt{9}$$, the radicand is 9.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The number inside the radical sign is called the radicand of the number. Hence, in  $$^3\\\\sqrt{9}$$, the radicand is 9.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The index of the radical number $$^5\\\\sqrt{4^3}$$ is equal to____.\",\n                    \"text\": \"The index of the radical number $$^5\\\\sqrt{4^3}$$ is equal to____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In the given number $$^5\\\\sqrt{4^3}$$,  the index of the radical is 5.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the given number $$^5\\\\sqrt{4^3}$$,  the index of the radical is 5.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the given number $$^5\\\\sqrt{4^3}$$,  the index of the radical is 5.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the given number $$^5\\\\sqrt{4^3}$$,  the index of the radical is 5.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In the given number $$^5\\\\sqrt{4^3}$$,  the index of the radical is 5.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In the given number $$^5\\\\sqrt{4^3}$$,  the index of the radical is 5.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Solve the radical equation: $$\\\\sqrt{x }\\\\;-\\\\;1 = 2$$\",\n                    \"text\": \"Solve the radical equation: $$\\\\sqrt{x }\\\\;-\\\\;1 = 2$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\sqrt{x} \\\\;-\\\\;1 = 2$$<br>\r\n$$\\\\sqrt{x} = 3$$\t\t\u2026isolate the radical<br>\r\n$$x = 9$$\t\t\t\u2026square both sides\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{x} \\\\;-\\\\;1 = 2$$<br>\r\n$$\\\\sqrt{x} = 3$$\t\t\u2026isolate the radical<br>\r\n$$x = 9$$\t\t\t\u2026square both sides\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{x} \\\\;-\\\\;1 = 2$$<br>\r\n$$\\\\sqrt{x} = 3$$\t\t\u2026isolate the radical<br>\r\n$$x = 9$$\t\t\t\u2026square both sides\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\sqrt{x} \\\\;-\\\\;1 = 2$$<br>\r\n$$\\\\sqrt{x} = 3$$\t\t\u2026isolate the radical<br>\r\n$$x = 9$$\t\t\t\u2026square both sides\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"9\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\sqrt{x} \\\\;-\\\\;1 = 2$$<br>\r\n$$\\\\sqrt{x} = 3$$\t\t\u2026isolate the radical<br>\r\n$$x = 9$$\t\t\t\u2026square both sides\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\sqrt{x} \\\\;-\\\\;1 = 2$$<br>\r\n$$\\\\sqrt{x} = 3$$\t\t\u2026isolate the radical<br>\r\n$$x = 9$$\t\t\t\u2026square both sides\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of \u201cx\u201d in the radical equation $$\\\\sqrt{2x} = 4$$ ?\",\n                    \"text\": \"What is the value of \u201cx\u201d in the radical equation $$\\\\sqrt{2x} = 4$$ ?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given: the radical equation $$\\\\sqrt{2x} = 4$$.<br>\r\nSquaring both sides, we get $$2x = 16 \\\\Rightarrow x = 8$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given: the radical equation $$\\\\sqrt{2x} = 4$$.<br>\r\nSquaring both sides, we get $$2x = 16 \\\\Rightarrow x = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given: the radical equation $$\\\\sqrt{2x} = 4$$.<br>\r\nSquaring both sides, we get $$2x = 16 \\\\Rightarrow x = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given: the radical equation $$\\\\sqrt{2x} = 4$$.<br>\r\nSquaring both sides, we get $$2x = 16 \\\\Rightarrow x = 8$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given: the radical equation $$\\\\sqrt{2x} = 4$$.<br>\r\nSquaring both sides, we get $$2x = 16 \\\\Rightarrow x = 8$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given: the radical equation $$\\\\sqrt{2x} = 4$$.<br>\r\nSquaring both sides, we get $$2x = 16 \\\\Rightarrow x = 8$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of \u201cm\u201d in the radical equation  $$^3\\\\sqrt{m} = 3$$ ?\",\n                    \"text\": \"What is the value of \u201cm\u201d in the radical equation  $$^3\\\\sqrt{m} = 3$$ ?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given: the radical equation  $$^3\\\\sqrt{m} = 3$$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$$m = 3^3 = 27$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given: the radical equation  $$^3\\\\sqrt{m} = 3$$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$$m = 3^3 = 27$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given: the radical equation  $$^3\\\\sqrt{m} = 3$$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$$m = 3^3 = 27$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"81\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given: the radical equation  $$^3\\\\sqrt{m} = 3$$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$$m = 3^3 = 27$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"27\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given: the radical equation  $$^3\\\\sqrt{m} = 3$$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$$m = 3^3 = 27$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given: the radical equation  $$^3\\\\sqrt{m} = 3$$.<br>\r\nTo eliminate cube root, cube both sides<br>\r\nWe get:<br>\r\n$$m = 3^3 = 27$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The equation $$\\\\sqrt{a\\\\;-\\\\;1} = \\\\;-3$$ has\",\n                    \"text\": \"The equation $$\\\\sqrt{a\\\\;-\\\\;1} = \\\\;-3$$ has\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $$\u22123$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"One solution\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $$\u22123$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"many solutions\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $$\u22123$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $$\u22123$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"No solution\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $$\u22123$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The principal square root of a number can only be positive. No value for a will give us a radical expression whose positive square root is $$\u22123$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-about-radical-equations\">Frequently Asked Questions about Radical Equations<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-947d9801-0f93-4b59-935b-d244a4e7758a\" 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-0-947d9801-0f93-4b59-935b-d244a4e7758a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-947d9801-0f93-4b59-935b-d244a4e7758a\"><strong>What is the radical equation in math?<\/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-0-947d9801-0f93-4b59-935b-d244a4e7758a\">\n\n<p class=\"eplus-wrapper\">An equation in which a variable is under a radical symbol (i.e.,$\\sqrt{} ,\\;^3\\sqrt{},\\; ^4\\sqrt{}$, etc.) is called a radical equation. For example, $\\sqrt{x} + 2 = 4$.<\/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-1-947d9801-0f93-4b59-935b-d244a4e7758a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-947d9801-0f93-4b59-935b-d244a4e7758a\"><strong>What are the n<sup>th<\/sup> root radicals?<\/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-1-947d9801-0f93-4b59-935b-d244a4e7758a\">\n\n<p class=\"eplus-wrapper\">The radical symbol $^n\\sqrt{x}$,or $x^\\frac{1}{n}$ , is called the n<sup>th<\/sup> root radical. The index for n<sup>th<\/sup> root radicals is n.<\/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-2-947d9801-0f93-4b59-935b-d244a4e7758a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-947d9801-0f93-4b59-935b-d244a4e7758a\"><strong>What is the formula for simplifying radicals?<\/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-2-947d9801-0f93-4b59-935b-d244a4e7758a\">\n\n<p class=\"eplus-wrapper\">The general formula for simplifying radicals is&nbsp; $^n\\sqrt{x}^m = x^\\frac{m}{n}$.<\/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-3-947d9801-0f93-4b59-935b-d244a4e7758a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-947d9801-0f93-4b59-935b-d244a4e7758a\"><strong>What is the use of radicals in real life?<\/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-3-947d9801-0f93-4b59-935b-d244a4e7758a\">\n\n<p class=\"eplus-wrapper\">European paper sizes are a good example of how a radical is used in real life. The ratio of the lengths of the longer and shorter sides of A4 paper is approximate $\\sqrt{2}$.<\/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-4-947d9801-0f93-4b59-935b-d244a4e7758a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-947d9801-0f93-4b59-935b-d244a4e7758a\"><strong>What are surds?<\/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-4-947d9801-0f93-4b59-935b-d244a4e7758a\">\n\n<p class=\"eplus-wrapper\">If the square root (or the cube root\/the n<sup>th<\/sup> root) of a number cannot be simplified into a whole number (W) or a rational number (\ud835\udd6b), we call it a surd. Examples: $\\sqrt{2},\\; \\sqrt{3},\\; ^3\\sqrt{11}$<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Radical Equations? Radical equations are equations in which a variable is under a radical symbol. Before we explore the concept of radical equations, let\u2019s quickly take a look at the important terminologies that will be helpful. Radical symbol: The symbol \u201c\u23b7\u201d that we use to denote square root, cube root, or nth root &#8230; <a title=\"Solving Radical Equations: Steps, Definition, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/radical-equations-solving\" aria-label=\"More on Solving Radical Equations: Steps, Definition, 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-27019","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\/27019","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=27019"}],"version-history":[{"count":13,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27019\/revisions"}],"predecessor-version":[{"id":39925,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27019\/revisions\/39925"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}