{"id":168393,"date":"2024-11-17T13:55:32","date_gmt":"2024-11-17T13:55:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168393"},"modified":"2024-11-17T13:55:35","modified_gmt":"2024-11-17T13:55:35","slug":"how-do-you-find-the-square-root-of-130-in-radical-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/17\/how-do-you-find-the-square-root-of-130-in-radical-form\/","title":{"rendered":"How do you find the square root of 130 in radical form"},"content":{"rendered":"\n<p>How do you find the square root of 130 in radical form?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the square root of ( 130 ) in radical form, we write it as ( \\sqrt{130} ). Since ( 130 ) is not a perfect square, its square root cannot be simplified to an integer. However, we can check if it can be simplified by factoring ( 130 ) into its prime factors.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Process:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Factorize ( 130 ):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factorization of ( 130 ) is ( 130 = 2 \\cdot 5 \\cdot 13 ).<\/li>\n\n\n\n<li>None of the factors ( 2, 5, ) or ( 13 ) are perfect squares.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Simplify the Radical:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In radical form, ( \\sqrt{130} ) does not simplify further because no pair of identical prime factors exists to &#8220;pull out&#8221; of the radical.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Verify Approximation:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\sqrt{130} ) is between ( \\sqrt{121} = 11 ) and ( \\sqrt{144} = 12 ), so its approximate value is slightly above 11.<\/li>\n\n\n\n<li>Using a calculator, ( \\sqrt{130} \\approx 11.4018 ).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Conclusion:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The exact square root of ( 130 ) in radical form remains ( \\sqrt{130} ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Detailed Explanation:<\/h3>\n\n\n\n<p>Radical simplification involves expressing a square root in its simplest form by identifying and factoring out perfect squares. For example, ( \\sqrt{18} = \\sqrt{9 \\cdot 2} = 3\\sqrt{2} ). This process is not possible with ( \\sqrt{130} ) because its prime factors ( 2, 5, ) and ( 13 ) do not form any perfect square products.<\/p>\n\n\n\n<p>In general, a square root that cannot be simplified further is called an &#8220;irrational number.&#8221; It remains in radical form, like ( \\sqrt{130} ), or is approximated using decimal values. While irrational numbers cannot be written exactly as decimals, they are crucial in mathematics, especially in geometry and algebra.<\/p>\n\n\n\n<p>Thus, the square root of ( 130 ) in radical form is <strong>( \\sqrt{130} )<\/strong>, and it does not simplify further.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How do you find the square root of 130 in radical form? The Correct Answer and Explanation is: To find the square root of ( 130 ) in radical form, we write it as ( \\sqrt{130} ). Since ( 130 ) is not a perfect square, its square root cannot be simplified to an integer. 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