To find the square root of 824, we’ll use the method of long division. Let’s break it down step by step:<\/p>\n\n\n\n
Step 1: Group the digits<\/h3>\n\n\n\n
Start by grouping the number into pairs of digits from right to left. In this case, 824 is grouped as:8\u2009248 \\, 24824<\/p>\n\n\n\n
Step 2: Find the largest number whose square is less than or equal to 8<\/h3>\n\n\n\n
Now, we look at the first group (8). The largest number whose square is less than or equal to 8 is 2, because 22=42^2 = 422=4, and 32=93^2 = 932=9 (which is too large). So, we write 2 as the first digit of our square root.<\/p>\n\n\n\n
Step 3: Subtract and bring down the next group<\/h3>\n\n\n\n
Now subtract 22=42^2 = 422=4 from 8:8\u22124=48 – 4 = 48\u22124=4<\/p>\n\n\n\n
Now, bring down the next pair of digits (24) next to 4, making it 424.<\/p>\n\n\n\n
Step 4: Double the current digit and find the next digit<\/h3>\n\n\n\n
Now, double the 2 (the first digit of our root) to get 4. Write it down as the divisor and leave a space next to it:4_(We will find the next digit here)4 \\_ \\quad \\text{(We will find the next digit here)}4_(We will find the next digit here)<\/p>\n\n\n\n
Now, guess a digit (let\u2019s call it ddd) that will complete the divisor and be multiplied by ddd such that 4d\u00d7d4d \\times d4d\u00d7d is less than or equal to 424. Try 8:48\u00d78=38448 \\times 8 = 38448\u00d78=384<\/p>\n\n\n\n
So, the next digit is 8. Now, we subtract:424\u2212384=40424 – 384 = 40424\u2212384=40<\/p>\n\n\n\n
Step 5: The final square root approximation<\/h3>\n\n\n\n
At this stage, we have found that the square root of 824 is approximately 28.8 (since the remainder is 40, and we would continue the process to get more precise digits).<\/p>\n\n\n\n
So, the square root of 824 is approximately:824\u224828.8\\sqrt{824} \\approx 28.8824\u200b\u224828.8<\/p>\n\n\n\n
This method is often used when you need a quick approximation, and while this result isn’t exact, it is close enough for many practical purposes. For more precision, you would continue with more steps of long division.<\/p>\n\n\n\n Find the square root of the following by finding the digit and the quotient. 824 The Correct Answer and Explanation is: To find the square root of 824, we’ll use the method of long division. Let’s break it down step by step: Step 1: Group the digits Start by grouping the number into pairs of […]<\/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-240579","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240579","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=240579"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240579\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240579"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240579"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240579"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-18.jpeg\")
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