{"id":245968,"date":"2025-07-06T15:27:53","date_gmt":"2025-07-06T15:27:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245968"},"modified":"2025-07-06T15:27:55","modified_gmt":"2025-07-06T15:27:55","slug":"find-the-square-root-of-the-6561-by-long-divison-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/find-the-square-root-of-the-6561-by-long-divison-method\/","title":{"rendered":"find the square root of the 6561 by long divison method"},"content":{"rendered":"\n<p>find the square root of the 6561 by long divison method<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the square root of 6561 by the long division method, follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Group the digits<\/h3>\n\n\n\n<p>Start by grouping the digits of the number into pairs, starting from the right. For 6561, the groups will be:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>65 and 61.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the first divisor<\/h3>\n\n\n\n<p>Find the largest number whose square is less than or equal to the first group (65). In this case, 8 * 8 = 64. So, the first divisor is 8.<\/p>\n\n\n\n<p>Write 8 as the first digit of the square root. Subtract 82=648^2 = 6482=64 from 65 to get the remainder:<\/p>\n\n\n\n<p>65 &#8211; 64 = 1.<\/p>\n\n\n\n<p>Bring down the next pair of digits (61), making the new number 161.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Double the divisor<\/h3>\n\n\n\n<p>Now, double the divisor (8) to get 16. This will be the first part of the new divisor.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the next digit<\/h3>\n\n\n\n<p>Now, you need to find a digit to append to the divisor. Consider the number you have (161). You need to find a digit ddd such that:(160+d)\u00d7d\u2264161(160 + d) \\times d \\leq 161(160+d)\u00d7d\u2264161<\/p>\n\n\n\n<p>Try d=1d = 1d=1:(160+1)\u00d71=161(160 + 1) \\times 1 = 161(160+1)\u00d71=161<\/p>\n\n\n\n<p>So, the next digit of the square root is 1.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Subtract and finish<\/h3>\n\n\n\n<p>Now, subtract 161161161 from 161161161 to get 0, and we are left with no remainder.<\/p>\n\n\n\n<p>Thus, the square root of 6561 is 81.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>6561=81\\sqrt{6561} = 816561\u200b=81<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The long division method for finding square roots involves iterative steps of guessing and refining the divisor. You start by grouping the digits and progressively find the largest possible divisor that works, adding one digit at a time. This process ensures an accurate square root is obtained, in this case, 81.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-759.jpeg\" alt=\"\" class=\"wp-image-245969\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>find the square root of the 6561 by long divison method The Correct Answer and Explanation is: To find the square root of 6561 by the long division method, follow these steps: Step 1: Group the digits Start by grouping the digits of the number into pairs, starting from the right. For 6561, the groups [&hellip;]<\/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-245968","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245968","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=245968"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245968\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}