{"id":279347,"date":"2025-08-03T18:25:22","date_gmt":"2025-08-03T18:25:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=279347"},"modified":"2025-08-03T18:25:25","modified_gmt":"2025-08-03T18:25:25","slug":"write-5frac-32-in-surd-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/03\/write-5frac-32-in-surd-form\/","title":{"rendered":"Write 5^(frac 3)2 in surd form."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-278.png\" alt=\"\" class=\"wp-image-279348\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>5\u221a5<\/strong>.<\/p>\n\n\n\n<p>To write the expression 5^(3\/2) in surd form, we need to understand the relationship between fractional exponents and radicals. The general rule for converting a fractional exponent to a surd is&nbsp;<strong>x^(a\/b) = \u1d47\u221a(x\u1d43)<\/strong>. In this rule, &#8216;x&#8217; is the base, &#8216;a&#8217; is the numerator of the exponent, and &#8216;b&#8217; is the denominator of the exponent. The denominator &#8216;b&#8217; becomes the index of the root, and the numerator &#8216;a&#8217; becomes the power of the base inside the root.<\/p>\n\n\n\n<p>Let&#8217;s apply this rule to the given expression, 5^(3\/2):<br>Here, the base (x) is 5.<br>The numerator of the exponent (a) is 3.<br>The denominator of the exponent (b) is 2.<\/p>\n\n\n\n<p>Substituting these values into the formula, we get:<br>5^(3\/2) = \u00b2\u221a(5\u00b3)<\/p>\n\n\n\n<p>A root with an index of 2 is a square root, which is typically written without the &#8216;2&#8217; in front of the radical symbol. So, the expression is:<br>\u221a(5\u00b3)<\/p>\n\n\n\n<p>Next, we calculate the value inside the radical. 5\u00b3 is equal to 5 \u00d7 5 \u00d7 5, which is 125.<br>So, our expression becomes:<br>\u221a125<\/p>\n\n\n\n<p>This is a correct surd, but it is not in its simplest form. To simplify a surd, we must find the largest perfect square that is a factor of the number inside the root (the radicand). For 125, the factors are 1, 5, 25, and 125. The largest perfect square factor is 25, because 5\u00b2 = 25.<\/p>\n\n\n\n<p>We can rewrite \u221a125 as the square root of the product of its factors:<br>\u221a125 = \u221a(25 \u00d7 5)<\/p>\n\n\n\n<p>Using the multiplication property of radicals, which states that \u221a(m \u00d7 n) = \u221am \u00d7 \u221an, we can split this into two separate roots:<br>\u221a(25 \u00d7 5) = \u221a25 \u00d7 \u221a5<\/p>\n\n\n\n<p>Since \u221a25 is equal to 5, we can simplify the expression to:<br>5 \u00d7 \u221a5<\/p>\n\n\n\n<p>Therefore, the final simplified surd form of 5^(3\/2) is 5\u221a5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner4-55.jpeg\" alt=\"\" class=\"wp-image-279349\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;5\u221a5. To write the expression 5^(3\/2) in surd form, we need to understand the relationship between fractional exponents and radicals. The general rule for converting a fractional exponent to a surd is&nbsp;x^(a\/b) = \u1d47\u221a(x\u1d43). In this rule, &#8216;x&#8217; is the base, &#8216;a&#8217; is the numerator of [&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-279347","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279347","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=279347"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279347\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=279347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=279347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=279347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}