{"id":146305,"date":"2024-09-30T17:34:47","date_gmt":"2024-09-30T17:34:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146305"},"modified":"2024-09-30T17:34:49","modified_gmt":"2024-09-30T17:34:49","slug":"square-root-of-24-using-perfect-squares","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/square-root-of-24-using-perfect-squares\/","title":{"rendered":"Square root of 24 using perfect squares"},"content":{"rendered":"\n<p>Square root of 24 using perfect squares<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the square root of 24 using perfect squares, we start by breaking down the number 24 into its prime factors. The prime factorization of 24 is:<\/p>\n\n\n\n<p>[<br>24 = 2^3 \\times 3^1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify Perfect Squares<\/h3>\n\n\n\n<p>Perfect squares are numbers that can be expressed as the square of an integer. The perfect squares less than 24 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1^2 = 1)<\/li>\n\n\n\n<li>(2^2 = 4)<\/li>\n\n\n\n<li>(3^2 = 9)<\/li>\n\n\n\n<li>(4^2 = 16)<\/li>\n<\/ul>\n\n\n\n<p>The largest perfect square that is less than 24 is 16.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Simplifying the Square Root<\/h3>\n\n\n\n<p>Using the perfect square 16, we can express the square root of 24 as follows:<\/p>\n\n\n\n<p>[<br>\\sqrt{24} = \\sqrt{16 \\times \\frac{24}{16}} = \\sqrt{16 \\times 1.5}<br>]<\/p>\n\n\n\n<p>This simplifies to:<\/p>\n\n\n\n<p>[<br>\\sqrt{24} = \\sqrt{16} \\times \\sqrt{1.5} = 4 \\times \\sqrt{1.5}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Approximating (\\sqrt{1.5})<\/h3>\n\n\n\n<p>To further simplify (\\sqrt{1.5}), we can use the fact that:<\/p>\n\n\n\n<p>[<br>1.5 = \\frac{3}{2}<br>]<\/p>\n\n\n\n<p>Thus:<\/p>\n\n\n\n<p>[<br>\\sqrt{1.5} = \\sqrt{\\frac{3}{2}} = \\frac{\\sqrt{3}}{\\sqrt{2}}<br>]<\/p>\n\n\n\n<p>Now, substituting this back into our equation, we have:<\/p>\n\n\n\n<p>[<br>\\sqrt{24} = 4 \\times \\frac{\\sqrt{3}}{\\sqrt{2}} = \\frac{4\\sqrt{3}}{\\sqrt{2}}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Final Simplification<\/h3>\n\n\n\n<p>To rationalize the denominator, we multiply the numerator and the denominator by (\\sqrt{2}):<\/p>\n\n\n\n<p>[<br>\\sqrt{24} = \\frac{4\\sqrt{3} \\times \\sqrt{2}}{2} = \\frac{4\\sqrt{6}}{2} = 2\\sqrt{6}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Therefore, the exact value of (\\sqrt{24}) can be expressed as:<\/p>\n\n\n\n<p>[<br>\\sqrt{24} = 2\\sqrt{6}<br>]<\/p>\n\n\n\n<p>For a numerical approximation, we can compute ( \\sqrt{6} ) to be approximately 2.45, giving us:<\/p>\n\n\n\n<p>[<br>\\sqrt{24} \\approx 2 \\times 2.45 \\approx 4.9<br>]<\/p>\n\n\n\n<p>Thus, we conclude that (\\sqrt{24} = 2\\sqrt{6} \\approx 4.9). This process highlights the importance of utilizing perfect squares to simplify square roots effectively.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Square root of 24 using perfect squares The Correct Answer and Explanation is : To find the square root of 24 using perfect squares, we start by breaking down the number 24 into its prime factors. The prime factorization of 24 is: [24 = 2^3 \\times 3^1] Step 1: Identify Perfect Squares Perfect squares are [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-146305","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=146305"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146305\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}