{"id":238450,"date":"2025-06-18T06:52:10","date_gmt":"2025-06-18T06:52:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238450"},"modified":"2025-06-18T06:52:13","modified_gmt":"2025-06-18T06:52:13","slug":"find-the-square-root-of-15-129-by-long-division-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/find-the-square-root-of-15-129-by-long-division-method\/","title":{"rendered":"find the square root of 15, 129 by long division method"},"content":{"rendered":"\n

find the square root of 15, 129 by long division method
<\/p>\n\n\n\n

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

The square root of 129<\/strong> lies between the two consecutive whole numbers 11<\/strong> and 12<\/strong>.<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

To estimate the square root of 129 without a calculator, begin by identifying perfect squares that are closest to 129. The perfect square just below 129 is 121<\/strong>, which is the square of 11<\/strong>. The perfect square just above 129 is 144<\/strong>, which is the square of 12<\/strong>. Since 129 is greater than 121 and less than 144, its square root must fall between 11 and 12.<\/p>\n\n\n\n

This means:<\/p>\n\n\n\n

    \n
  • 112=12111^2 = 121112=121<\/li>\n\n\n\n
  • 122=14412^2 = 144122=144<\/li>\n\n\n\n
  • 129\\sqrt{129}129\u200b is greater than 11 because 129 is greater than 121.<\/li>\n\n\n\n
  • 129\\sqrt{129}129\u200b is less than 12 because 129 is less than 144.<\/li>\n<\/ul>\n\n\n\n

    Thus, the square root of 129 lies between 11 and 12.<\/p>\n\n\n\n

    To make this estimate more precise without calculating the exact square root, consider the midpoint:<\/p>\n\n\n\n

      \n
    • Try 11.5: 11.52=132.2511.5^2 = 132.2511.52=132.25, which is more than 129.<\/li>\n\n\n\n
    • Try 11.3: 11.32=127.6911.3^2 = 127.6911.32=127.69, which is slightly less than 129.<\/li>\n\n\n\n
    • Try 11.4: 11.42=129.9611.4^2 = 129.9611.42=129.96, which is very close but a little over 129.<\/li>\n<\/ul>\n\n\n\n

      From this trial method, it becomes clear that 129\u224811.36\\sqrt{129} \\approx 11.36129\u200b\u224811.36, which confirms it falls between 11 and 12.<\/p>\n\n\n\n

      However, since the question asks for two consecutive whole numbers<\/strong> between which the square root lies, the answer is 11 and 12<\/strong>.<\/p>\n\n\n\n

      This estimation technique is useful in many real-life situations where rough values are more practical or accessible than precise values, especially in mental math, standardized tests, or scientific approximations.<\/p>\n\n\n\n

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

      find the square root of 15, 129 by long division method The Correct Answer and Explanation is: The square root of 129 lies between the two consecutive whole numbers 11 and 12. Explanation To estimate the square root of 129 without a calculator, begin by identifying perfect squares that are closest to 129. The perfect […]<\/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-238450","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238450","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=238450"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238450\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}