{"id":245996,"date":"2025-07-06T17:05:56","date_gmt":"2025-07-06T17:05:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245996"},"modified":"2025-07-06T17:05:58","modified_gmt":"2025-07-06T17:05:58","slug":"find-the-square-root-of-the-following-number-by-the-prime-factorisation-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/find-the-square-root-of-the-following-number-by-the-prime-factorisation-method\/","title":{"rendered":"Find the square root of the following number by the prime factorisation method"},"content":{"rendered":"\n

Find the square root of the following number by the prime factorisation method. 5929<\/p>\n\n\n\n

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

To find the square root of 5929 using the prime factorization method, we need to express the number as a product of prime factors and then group the factors in pairs.<\/p>\n\n\n\n

Step-by-Step Solution:<\/h3>\n\n\n\n
    \n
  1. Divide the number by the smallest prime number (2, 3, 5, 7, 11, etc.)<\/strong> until you can no longer divide. Start by checking divisibility by the smallest primes:\n
      \n
    • 5929 is odd, so it is not divisible by 2.<\/li>\n\n\n\n
    • Sum of the digits of 5929: 5+9+2+9=255 + 9 + 2 + 9 = 255+9+2+9=25. Since 25 is not divisible by 3, 5929 is not divisible by 3.<\/li>\n\n\n\n
    • 5929 does not end in 0 or 5, so it is not divisible by 5.<\/li>\n\n\n\n
    • Check divisibility by 7. Divide 5929 by 7: 5929\u00f77=8475929 \u00f7 7 = 8475929\u00f77=847 So, 5929 can be divided by 7. We now have: 5929=7\u00d78475929 = 7 \u00d7 8475929=7\u00d7847<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Factor 847 further<\/strong>: Now, check if 847 is divisible by any prime numbers:\n
        \n
      • 847 is odd, so not divisible by 2.<\/li>\n\n\n\n
      • Sum of the digits of 847: 8+4+7=198 + 4 + 7 = 198+4+7=19, which is not divisible by 3.<\/li>\n\n\n\n
      • 847 does not end in 0 or 5, so not divisible by 5.<\/li>\n\n\n\n
      • Check divisibility by 7: 847\u00f77=121847 \u00f7 7 = 121847\u00f77=121 So, we now have: 847=7\u00d7121847 = 7 \u00d7 121847=7\u00d7121 Thus, we have: 5929=7\u00d77\u00d71215929 = 7 \u00d7 7 \u00d7 1215929=7\u00d77\u00d7121<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Factor 121 further<\/strong>: 121 is a perfect square: 121=11\u00d711121 = 11 \u00d7 11121=11\u00d711<\/li>\n\n\n\n
      • Prime factorization of 5929<\/strong>:
        Combining all the factors, we get: 5929=7\u00d77\u00d711\u00d7115929 = 7 \u00d7 7 \u00d7 11 \u00d7 115929=7\u00d77\u00d711\u00d711 Or, in exponential form: 5929=72\u00d71125929 = 7^2 \u00d7 11^25929=72\u00d7112<\/li>\n\n\n\n
      • Find the square root<\/strong>: The square root of a number is obtained by taking the square root of each factor: 5929=72\u00d7112=7\u00d711=77\\sqrt{5929} = \\sqrt{7^2 \u00d7 11^2} = 7 \u00d7 11 = 775929\u200b=72\u00d7112\u200b=7\u00d711=77<\/li>\n<\/ol>\n\n\n\n

        Conclusion:<\/h3>\n\n\n\n

        The square root of 5929 is 77<\/strong>.<\/p>\n\n\n\n

        This method works because when you factorize a number and group the prime factors in pairs, you can take one factor from each pair to find the square root.<\/p>\n\n\n\n

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

        Find the square root of the following number by the prime factorisation method. 5929 The Correct Answer and Explanation is: To find the square root of 5929 using the prime factorization method, we need to express the number as a product of prime factors and then group the factors in pairs. Step-by-Step Solution: Conclusion: The […]<\/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-245996","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245996","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=245996"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245996\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}