{"id":253021,"date":"2025-07-11T17:02:09","date_gmt":"2025-07-11T17:02:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253021"},"modified":"2025-07-11T17:02:14","modified_gmt":"2025-07-11T17:02:14","slug":"by-what-number-5000-should-be-multiplied-to-become-a-perfect-square-and-find-the-square-root-of-result-number","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/by-what-number-5000-should-be-multiplied-to-become-a-perfect-square-and-find-the-square-root-of-result-number\/","title":{"rendered":"By what number 5000 should be multiplied to become a perfect square and find the square root of result number"},"content":{"rendered":"\n<p>By what number 5000 should be multiplied to become a perfect square and find the square root of result number<\/p>\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>To find the number by which 5000 should be multiplied to become a perfect square, let&#8217;s go through the steps systematically.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization of 5000<\/h3>\n\n\n\n<p>Start by performing the prime factorization of 5000: 5000\u00f72=2500(divideby2)5000 \\div 2 = 2500 \\quad (divide by 2)5000\u00f72=2500(divideby2) 2500\u00f72=1250(divideby2)2500 \\div 2 = 1250 \\quad (divide by 2)2500\u00f72=1250(divideby2) 1250\u00f72=625(divideby2)1250 \\div 2 = 625 \\quad (divide by 2)1250\u00f72=625(divideby2)<\/p>\n\n\n\n<p>Now divide by 5: 625\u00f75=125625 \\div 5 = 125625\u00f75=125 125\u00f75=25125 \\div 5 = 25125\u00f75=25 25\u00f75=525 \\div 5 = 525\u00f75=5 5\u00f75=15 \\div 5 = 15\u00f75=1<\/p>\n\n\n\n<p>So, the prime factorization of 5000 is: 5000=23\u00d7545000 = 2^3 \\times 5^45000=23\u00d754<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Analyze the Exponents<\/h3>\n\n\n\n<p>To make 5000 a perfect square, each exponent in its prime factorization must be even. Currently, the exponents are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>232^323 (odd exponent),<\/li>\n\n\n\n<li>545^454 (even exponent).<\/li>\n<\/ul>\n\n\n\n<p>To make the number a perfect square, we need to balance the odd exponent of 2. Specifically, we need to multiply by one more factor of 2 to make the exponent of 2 even (i.e., 242^424).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Multiply 5000 by 2<\/h3>\n\n\n\n<p>Thus, we need to multiply 5000 by 2: 5000\u00d72=100005000 \\times 2 = 100005000\u00d72=10000<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the Square Root of 10000<\/h3>\n\n\n\n<p>Now, to find the square root of the result, 10000\\sqrt{10000}10000\u200b: 10000=100\\sqrt{10000} = 10010000\u200b=100<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The number that 5000 should be multiplied by is 2.<\/li>\n\n\n\n<li>The square root of 10000 is 100.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>By multiplying 5000 by 2, we ensure that each prime factor&#8217;s exponent becomes even, making the number a perfect square. The square root of 10000 is then the integer 100, which is the final answer<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-321.jpeg\" alt=\"\" class=\"wp-image-253022\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>By what number 5000 should be multiplied to become a perfect square and find the square root of result number The Correct Answer and Explanation is: To find the number by which 5000 should be multiplied to become a perfect square, let&#8217;s go through the steps systematically. Step 1: Prime Factorization of 5000 Start by [&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-253021","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253021","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=253021"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253021\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}