{"id":250921,"date":"2025-07-10T13:15:48","date_gmt":"2025-07-10T13:15:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=250921"},"modified":"2025-07-10T13:15:50","modified_gmt":"2025-07-10T13:15:50","slug":"find-the-square-root-of-144-by-repeated-subtraction-prime-factorization-and-long-division-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/find-the-square-root-of-144-by-repeated-subtraction-prime-factorization-and-long-division-method\/","title":{"rendered":"Find the square root of 144 by repeated subtraction, prime factorization and long division method"},"content":{"rendered":"\n

Find the square root of 144 by repeated subtraction, prime factorization and long division method<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the square root of 144 using three different methods, here’s how it’s done:<\/p>\n\n\n\n

1. Repeated Subtraction Method:<\/strong><\/h3>\n\n\n\n

This method works by subtracting successive odd numbers from the given number (144) until you reach zero. The number of subtractions gives you the square root.<\/p>\n\n\n\n

    \n
  • Start with 144.<\/li>\n\n\n\n
  • Subtract 1 (the first odd number).<\/li>\n\n\n\n
  • Subtract 3 (the second odd number).<\/li>\n\n\n\n
  • Continue subtracting 5, 7, 9, 11, etc., increasing the odd number by 2 each time.<\/li>\n\n\n\n
  • After 12 subtractions, you will reach zero, and the number of subtractions (12) is the square root of 144.<\/li>\n<\/ul>\n\n\n\n

    Thus, the square root of 144 is 12.<\/p>\n\n\n\n

    2. Prime Factorization Method:<\/strong><\/h3>\n\n\n\n

    To use prime factorization, break the number into prime factors and then group them in pairs.<\/p>\n\n\n\n

      \n
    • Start by dividing 144 by the smallest prime, 2.<\/li>\n\n\n\n
    • 144 \u00f7 2 = 72.<\/li>\n\n\n\n
    • 72 \u00f7 2 = 36.<\/li>\n\n\n\n
    • 36 \u00f7 2 = 18.<\/li>\n\n\n\n
    • 18 \u00f7 2 = 9.<\/li>\n\n\n\n
    • 9 \u00f7 3 = 3.<\/li>\n\n\n\n
    • 3 \u00f7 3 = 1.<\/li>\n<\/ul>\n\n\n\n

      Now, the prime factorization of 144 is:
      144=24\u00d732144 = 2^4 \\times 3^2<\/p>\n\n\n\n

      To find the square root, take the square root of each pair of prime factors:<\/p>\n\n\n\n

        \n
      • Square root of 242^4 is 22=42^2 = 4.<\/li>\n\n\n\n
      • Square root of 323^2 is 33.<\/li>\n<\/ul>\n\n\n\n

        Multiply these results:
        4\u00d73=124 \\times 3 = 12<\/p>\n\n\n\n

        Thus, the square root of 144 is 12.<\/p>\n\n\n\n

        3. Long Division Method:<\/strong><\/h3>\n\n\n\n

        This method involves dividing the number into groups of two digits from right to left, then using successive division and subtraction.<\/p>\n\n\n\n

          \n
        • Group 144 as (1) (44).<\/li>\n\n\n\n
        • Find the largest number whose square is less than or equal to the first group (1). The answer is 1, so subtract 12=11^2 = 1 from 1. The remainder is 0.<\/li>\n\n\n\n
        • Bring down the next group, 44. Now, double the divisor (which is 1) to get 2.<\/li>\n\n\n\n
        • Find a number that, when placed next to 2, and multiplied by the same number, gives a result close to 44. This number is 2. Multiply 22 by 2 to get 44. Subtract 44 from 44. The remainder is 0.<\/li>\n<\/ul>\n\n\n\n

          Since no remainder is left, the square root is 12.<\/p>\n\n\n\n

          Thus, the square root of 144 is 12.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Find the square root of 144 by repeated subtraction, prime factorization and long division method The correct answer and explanation is: To find the square root of 144 using three different methods, here’s how it’s done: 1. Repeated Subtraction Method: This method works by subtracting successive odd numbers from the given number (144) until you […]<\/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-250921","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250921","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=250921"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250921\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250921"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250921"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}