Let’s break down the question step by step.<\/p>\n\n\n\n
1. Is 300 a perfect square?<\/h3>\n\n\n\n
A perfect square is a number that can be expressed as the square of an integer. In other words, if the square root of a number is an integer, then the number is a perfect square.<\/p>\n\n\n\n
The square root of 300 is approximately:300\u224817.32\\sqrt{300} \\approx 17.32300\u200b\u224817.32<\/p>\n\n\n\n
Since this is not an integer, 300 is not a perfect square<\/strong>.<\/p>\n\n\n\n To find the smallest multiple of 300 that is a perfect square, we need to identify the prime factorization of 300 and adjust it to make sure that all exponents of the prime factors are even (since a perfect square requires all prime factors to appear with an even exponent).<\/p>\n\n\n\n Prime factorization of 300:300=22\u00d73\u00d752300 = 2^2 \\times 3 \\times 5^2300=22\u00d73\u00d752<\/p>\n\n\n\n For a perfect square, the exponents of all prime factors must be even. Here, the exponent of 3 is odd, so we need to multiply by 3 to make the exponent of 3 even. Thus, the smallest multiple of 300 that is a perfect square is:300\u00d73=900300 \\times 3 = 900300\u00d73=900<\/p>\n\n\n\n Now, let’s factorize 1,458:1458=2\u00d733\u00d771458 = 2 \\times 3^3 \\times 71458=2\u00d733\u00d77<\/p>\n\n\n\n For this number to be a perfect square, we need to make the exponents of all prime factors even. Currently, the exponents of 2, 3, and 7 are all odd. Therefore, we need to multiply by 2\u00d73\u00d77=422 \\times 3 \\times 7 = 422\u00d73\u00d77=42 to make all exponents even. Thus, the smallest number by which 1,458 should be multiplied is 42.<\/p>\n\n\n\n After multiplying:1458\u00d742=612361458 \\times 42 = 612361458\u00d742=61236<\/p>\n\n\n\n Let’s check the square root of 61236:61236=246\\sqrt{61236} = 24661236\u200b=246<\/p>\n\n\n\n So, the perfect square is 61236, and its square root is 246.<\/p>\n\n\n\n Is 300 a perfect square? If not, find the smallest multiple whose square root is the number obtained. Find the smallest number by which 1,458 should be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained. The Correct Answer and Explanation is: Let’s break down the question […]<\/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-245736","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245736","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=245736"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245736\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}2. Find the smallest multiple whose square root is the number obtained.<\/h3>\n\n\n\n
3. Find the smallest number by which 1,458 should be multiplied to get a perfect square.<\/h3>\n\n\n\n
Final Answers:<\/h3>\n\n\n\n
\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-703.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"