{"id":227838,"date":"2025-06-06T14:23:22","date_gmt":"2025-06-06T14:23:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227838"},"modified":"2025-06-06T14:23:23","modified_gmt":"2025-06-06T14:23:23","slug":"using-prime-factorisation-method-find-the-cube-root-of-1024-x-8788","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/using-prime-factorisation-method-find-the-cube-root-of-1024-x-8788\/","title":{"rendered":"Using prime factorisation method, find the cube root of 1024 x 8788."},"content":{"rendered":"\n

Using prime factorisation method, find the cube root of 1024 x 8788.<\/p>\n\n\n\n

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

\u2705 Answer:<\/h3>\n\n\n\n

Using prime factorization<\/strong>, the cube root of 1024\u00d787881024 \\times 87881024\u00d78788 is:1024\u00d787883=213\u00d722\u00d71093=215\u00d71093\\sqrt[3]{1024 \\times 8788} = \\sqrt[3]{2^{13} \\times 2^2 \\times 109} = \\sqrt[3]{2^{15} \\times 109}31024\u00d78788\u200b=3213\u00d722\u00d7109\u200b=3215\u00d7109\u200b<\/p>\n\n\n\n

Now simplify:215\u00d71093=25\u00d71093=32\u00d71093\\sqrt[3]{2^{15} \\times 109} = 2^5 \\times \\sqrt[3]{109} = 32 \\times \\sqrt[3]{109}3215\u00d7109\u200b=25\u00d73109\u200b=32\u00d73109\u200b<\/p>\n\n\n\n

\ud83d\udfe9 Final Answer:<\/strong> 32\u00d71093\\boxed{32 \\times \\sqrt[3]{109}}32\u00d73109\u200b\u200b (This is the simplest exact form)<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udcd8 Detailed Explanation <\/h3>\n\n\n\n

To find the cube root of 1024\u00d787881024 \\times 87881024\u00d78788 using prime factorization<\/strong>, we first factorize each number into its prime components.<\/p>\n\n\n\n

Step 1: Prime factorization of 1024<\/h4>\n\n\n\n

1024=2\u00d72\u00d72\u00d7\u2026(10 times)=2101024 = 2 \\times 2 \\times 2 \\times \\dots \\text{(10 times)} = 2^{10}1024=2\u00d72\u00d72\u00d7\u2026(10 times)=210<\/p>\n\n\n\n

Step 2: Prime factorization of 8788<\/h4>\n\n\n\n

Let’s divide 8788 by 2 (smallest prime number):8788\u00f72=43944394\u00f72=21978788 \\div 2 = 4394 \\\\ 4394 \\div 2 = 21978788\u00f72=43944394\u00f72=2197<\/p>\n\n\n\n

Now check 2197. It\u2019s not divisible by 2, 3, or 7. Try 13:13\u00d7169=219713 \\times 169 = 219713\u00d7169=2197<\/p>\n\n\n\n

Then:13\u00d713=169\u21d213\u00d713\u00d713=2197\u21d22197=13313 \\times 13 = 169 \\Rightarrow 13 \\times 13 \\times 13 = 2197 \\Rightarrow 2197 = 13^313\u00d713=169\u21d213\u00d713\u00d713=2197\u21d22197=133<\/p>\n\n\n\n

So,8788=22\u00d71338788 = 2^2 \\times 13^38788=22\u00d7133<\/p>\n\n\n\n

Step 3: Multiply the two numbers:<\/h4>\n\n\n\n

1024\u00d78788=210\u00d7(22\u00d7133)=212\u00d71331024 \\times 8788 = 2^{10} \\times (2^2 \\times 13^3) = 2^{12} \\times 13^31024\u00d78788=210\u00d7(22\u00d7133)=212\u00d7133<\/p>\n\n\n\n

Now take the cube root<\/strong>:212\u00d71333=(24)3\u00d71333=24\u00d713=16\u00d713=208\\sqrt[3]{2^{12} \\times 13^3} = \\sqrt[3]{(2^4)^3 \\times 13^3} = 2^4 \\times 13 = 16 \\times 13 = \\boxed{208}3212\u00d7133\u200b=3(24)3\u00d7133\u200b=24\u00d713=16\u00d713=208\u200b<\/p>\n\n\n\n

\ud83d\udd01 Correction to earlier steps: I mistakenly used 109 before \u2014 the actual prime factor of 8788 is 13<\/strong>, not 109.<\/p>\n\n\n\n

\n\n\n\n

\u2705 Correct Final Answer: 208\\boxed{208}208\u200b<\/h3>\n\n\n\n

This method shows how breaking down large numbers into their prime factors allows for easy root extraction by grouping exponents into multiples of 3.<\/p>\n\n\n\n

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

Using prime factorisation method, find the cube root of 1024 x 8788. The Correct Answer and Explanation is: \u2705 Answer: Using prime factorization, the cube root of 1024\u00d787881024 \\times 87881024\u00d78788 is:1024\u00d787883=213\u00d722\u00d71093=215\u00d71093\\sqrt[3]{1024 \\times 8788} = \\sqrt[3]{2^{13} \\times 2^2 \\times 109} = \\sqrt[3]{2^{15} \\times 109}31024\u00d78788\u200b=3213\u00d722\u00d7109\u200b=3215\u00d7109\u200b Now simplify:215\u00d71093=25\u00d71093=32\u00d71093\\sqrt[3]{2^{15} \\times 109} = 2^5 \\times \\sqrt[3]{109} = 32 \\times \\sqrt[3]{109}3215\u00d7109\u200b=25\u00d73109\u200b=32\u00d73109\u200b […]<\/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-227838","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227838","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=227838"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227838\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}