{"id":168925,"date":"2024-11-18T18:17:23","date_gmt":"2024-11-18T18:17:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168925"},"modified":"2024-11-18T18:17:26","modified_gmt":"2024-11-18T18:17:26","slug":"x3-5-write-the-expression-in-a-radical-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/18\/x3-5-write-the-expression-in-a-radical-form\/","title":{"rendered":"X3\/5 write the expression in a radical form"},"content":{"rendered":"\n<p>X3\/5 write the expression in a radical form<\/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 express ( \\frac{3}{5} ) as a radical, we aim to rewrite the expression in a form involving a radical symbol (square root, cube root, etc.). In this case, we\u2019ll rewrite ( \\frac{3}{5} ) using a radical for the exponent.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Recall exponent rules<\/h3>\n\n\n\n<p>We know that ( a^b ) can be written as a radical as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( a^b = \\sqrt[b]{a} ), where ( a ) is the base and ( b ) is the exponent.<\/li>\n<\/ul>\n\n\n\n<p>For ( \\frac{3}{5} ), we recognize that this is a fractional exponent. We can rewrite it as:<\/p>\n\n\n\n<p>[<br>\\left( a^{\\frac{3}{5}} \\right) = \\sqrt[5]{a^3}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Applying to the given expression<\/h3>\n\n\n\n<p>For the expression ( \\frac{3}{5} ), we apply the same principle. We can express it as a radical with the following steps:<\/p>\n\n\n\n<p>[<br>\\frac{3}{5} = 3^{\\frac{3}{5}} = \\sqrt[5]{3^3} = \\sqrt[5]{27}<br>]<\/p>\n\n\n\n<p>So, ( \\frac{3}{5} ) written as a radical is ( \\sqrt[5]{27} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of steps:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Fractional Exponent Rule<\/strong>: We start by noting that a fractional exponent like ( \\frac{m}{n} ) can be rewritten as ( a^{\\frac{m}{n}} = \\sqrt[n]{a^m} ).<\/li>\n\n\n\n<li><strong>Apply the rule<\/strong>: For ( \\frac{3}{5} ), this means the expression becomes ( 3^{\\frac{3}{5}} ), which we convert into the radical form ( \\sqrt[5]{3^3} ).<\/li>\n\n\n\n<li><strong>Simplify the exponent<\/strong>: Since ( 3^3 = 27 ), the final result is ( \\sqrt[5]{27} ).<\/li>\n<\/ol>\n\n\n\n<p>Thus, the expression ( \\frac{3}{5} ) in radical form is ( \\sqrt[5]{27} ). This radical represents the fifth root of 27, which is the equivalent of taking ( 3^{\\frac{3}{5}} ) in its fractional exponent form.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>In summary, expressing ( \\frac{3}{5} ) as a radical involves rewriting the fractional exponent as a root. The expression ( 3^{\\frac{3}{5}} ) becomes ( \\sqrt[5]{27} ), which is the correct radical form of the given expression.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>X3\/5 write the expression in a radical form The Correct Answer and Explanation is : To express ( \\frac{3}{5} ) as a radical, we aim to rewrite the expression in a form involving a radical symbol (square root, cube root, etc.). In this case, we\u2019ll rewrite ( \\frac{3}{5} ) using a radical for the exponent. [&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-168925","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168925","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=168925"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168925\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}