{"id":230854,"date":"2025-06-10T07:02:52","date_gmt":"2025-06-10T07:02:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230854"},"modified":"2025-06-10T07:02:54","modified_gmt":"2025-06-10T07:02:54","slug":"find-the-square-root-of-the-following-numbers-by-the-prime-factorisation-method-ix-8100-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/10\/find-the-square-root-of-the-following-numbers-by-the-prime-factorisation-method-ix-8100-2\/","title":{"rendered":"Find the square root of the following numbers by the prime factorisation method ( ix ) 8100"},"content":{"rendered":"\n

Find the square root of the following numbers by the prime factorisation method ( ix ) 8100<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the square root of 8100<\/strong> using the prime factorisation method<\/strong>, follow these steps:<\/p>\n\n\n\n

\n\n\n\n

\u2705 Step-by-step Prime Factorisation of 8100<\/strong>:<\/h3>\n\n\n\n

Start by dividing 8100 by the smallest prime numbers:<\/p>\n\n\n\n

    \n
  1. 8100\u00f72=40508100 \\div 2 = 40508100\u00f72=4050<\/li>\n\n\n\n
  2. 4050\u00f72=20254050 \\div 2 = 20254050\u00f72=2025<\/li>\n\n\n\n
  3. 2025\u00f73=6752025 \\div 3 = 6752025\u00f73=675<\/li>\n\n\n\n
  4. 675\u00f73=225675 \\div 3 = 225675\u00f73=225<\/li>\n\n\n\n
  5. 225\u00f73=75225 \\div 3 = 75225\u00f73=75<\/li>\n\n\n\n
  6. 75\u00f73=2575 \\div 3 = 2575\u00f73=25<\/li>\n\n\n\n
  7. 25\u00f75=525 \\div 5 = 525\u00f75=5<\/li>\n\n\n\n
  8. 5\u00f75=15 \\div 5 = 15\u00f75=1<\/li>\n<\/ol>\n\n\n\n

    Now write the prime factorisation: 8100=22\u00d734\u00d7528100 = 2^2 \\times 3^4 \\times 5^28100=22\u00d734\u00d752<\/p>\n\n\n\n

    \n\n\n\n

    \u2705 Finding the Square Root<\/strong>:<\/h3>\n\n\n\n

    To find the square root, pair up the prime factors: 8100=22\u00d734\u00d752=2\u00d732\u00d75=2\u00d79\u00d75=90\\sqrt{8100} = \\sqrt{2^2 \\times 3^4 \\times 5^2} = 2 \\times 3^2 \\times 5 = 2 \\times 9 \\times 5 = 908100\u200b=22\u00d734\u00d752\u200b=2\u00d732\u00d75=2\u00d79\u00d75=90<\/p>\n\n\n\n

    \n\n\n\n

    \ud83c\udfaf Final Answer<\/strong>:<\/h3>\n\n\n\n

    8100=90\\sqrt{8100} = \\boxed{90}8100\u200b=90\u200b<\/p>\n\n\n\n

    \n\n\n\n

    \ud83d\udcd8 Explanation<\/strong><\/h3>\n\n\n\n

    The prime factorisation method<\/strong> is a systematic approach to finding the square root of a number by expressing it as a product of prime numbers. The idea is to break the number down into its basic building blocks \u2014 its prime factors<\/strong> \u2014 and then use the rules of square roots to simplify.<\/p>\n\n\n\n

    In the case of 8100<\/strong>, we start by dividing it by the smallest prime number, which is 2<\/strong>, and continue dividing by prime numbers like 3<\/strong> and 5<\/strong> until we reach 1. This gives us: 8100=22\u00d734\u00d7528100 = 2^2 \\times 3^4 \\times 5^28100=22\u00d734\u00d752<\/p>\n\n\n\n

    Next, we take the square root<\/strong>. Since we are finding the square root, we look for pairs of prime factors. Each pair of the same prime number<\/strong> contributes one of that prime<\/strong> to the square root.<\/p>\n\n\n\n

    For instance, 222^222 becomes 222, 343^434 becomes 32=93^2 = 932=9, and 525^252 becomes 555. Multiply these results: 2\u00d79\u00d75=902 \\times 9 \\times 5 = 902\u00d79\u00d75=90<\/p>\n\n\n\n

    Therefore, the square root of 8100 is 90<\/strong>.<\/p>\n\n\n\n

    This method is particularly useful for perfect squares, as the factorisation ensures all primes occur in even powers. If a prime factor doesn’t form a complete pair, then the number is not<\/strong> a perfect square. In this case, since all exponents were even, 8100 is a perfect square, and its root is an integer: 90<\/strong>.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Find the square root of the following numbers by the prime factorisation method ( ix ) 8100 The Correct Answer and Explanation is: To find the square root of 8100 using the prime factorisation method, follow these steps: \u2705 Step-by-step Prime Factorisation of 8100: Start by dividing 8100 by the smallest prime numbers: Now write […]<\/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-230854","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230854","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=230854"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230854\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}