To find the cube root of 64000 using prime factorization, we need to break down the number into its prime factors and then identify the cube root.<\/p>\n\n\n\n
Step 1: Prime Factorization of 64000<\/h3>\n\n\n\n
We start by dividing 64000 by the smallest prime number, which is 2: 64000\u00f72=3200064000 \\div 2 = 3200064000\u00f72=32000 32000\u00f72=1600032000 \\div 2 = 1600032000\u00f72=16000 16000\u00f72=800016000 \\div 2 = 800016000\u00f72=8000 8000\u00f72=40008000 \\div 2 = 40008000\u00f72=4000 4000\u00f72=20004000 \\div 2 = 20004000\u00f72=2000 2000\u00f72=10002000 \\div 2 = 10002000\u00f72=1000 1000\u00f72=5001000 \\div 2 = 5001000\u00f72=500 500\u00f72=250500 \\div 2 = 250500\u00f72=250 250\u00f72=125250 \\div 2 = 125250\u00f72=125<\/p>\n\n\n\n
Now, 125 is not divisible by 2, so we move to the next smallest prime number, which is 5: 125\u00f75=25125 \\div 5 = 25125\u00f75=25 25\u00f75=525 \\div 5 = 525\u00f75=5 5\u00f75=15 \\div 5 = 15\u00f75=1<\/p>\n\n\n\n
So, the prime factorization of 64000 is: 64000=28\u00d75364000 = 2^8 \\times 5^364000=28\u00d753<\/p>\n\n\n\n
Step 2: Taking the Cube Root<\/h3>\n\n\n\n
The cube root of a number can be found by taking the cube root of each factor in the prime factorization. In this case, we have 282^828 and 535^353.<\/p>\n\n\n\n
For 282^828, we can rewrite it as: 28=(23)2\u00d7222^8 = (2^3)^2 \\times 2^228=(23)2\u00d722<\/p>\n\n\n\n
Thus, the cube root of 282^828 is 222^222, because the cube root of 232^323 is just 2. The remaining factor 222^222 will be left as a square.<\/p>\n\n\n\n
For 535^353, the cube root of 535^353 is simply 5, because the cube root of 535^353 is 5.<\/p>\n\n\n\n
Thus, we now have: 640003=28\u00d7533=22\u00d75=4\u00d75=20\\sqrt[3]{64000} = \\sqrt[3]{2^8 \\times 5^3} = 2^2 \\times 5 = 4 \\times 5 = 20364000\u200b=328\u00d753\u200b=22\u00d75=4\u00d75=20<\/p>\n\n\n\n
Step 3: Final Answer<\/h3>\n\n\n\n
The cube root of 64000 is 202020.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
Prime factorization involves breaking down a number into its prime factors. In this case, 64000 is factored as 28\u00d7532^8 \\times 5^328\u00d753. When finding the cube root, we take the cube root of each factor. The cube root of 282^828 is 222^222, and the cube root of 535^353 is 5. The final result is the product of these values, which gives 20.<\/p>\n\n\n\n
Thus, the cube root of 64000 is 202020.<\/p>\n\n\n\n Cube root of each of the following by prime factorization: 64000 (full process) The Correct Answer and Explanation is: To find the cube root of 64000 using prime factorization, we need to break down the number into its prime factors and then identify the cube root. Step 1: Prime Factorization of 64000 We start by […]<\/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-255482","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255482","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=255482"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255482\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=255482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=255482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=255482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-447.jpeg\")
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