{"id":248696,"date":"2025-07-08T16:45:19","date_gmt":"2025-07-08T16:45:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248696"},"modified":"2025-07-08T16:45:21","modified_gmt":"2025-07-08T16:45:21","slug":"the-solution-to-the-equation-x364-is-called-the-cube-root-of-64","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/the-solution-to-the-equation-x364-is-called-the-cube-root-of-64\/","title":{"rendered":"The solution to the equation\u00a0x3=64\u00a0is called the cube root of 64"},"content":{"rendered":"\n
The solution to the equation x3=64 is called the cube root of 64<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Here are the correct answers to the expressions:<\/p>\n\n\n\n
a. 4
b. 5
c. -2<\/p>\n\n\n\n
Explanation<\/strong><\/p>\n\n\n\n
The problem asks us to evaluate several cube roots based on the provided definition. A cube root of a number is a special value that, when multiplied by itself three times, results in the original number. This operation is the inverse of cubing a number. For example, the solution to the equation x\u00b3 = 64 is the cube root of 64. We will apply this principle to solve each part of the question.<\/p>\n\n\n\n
a. \u00b3\u221a64<\/strong>
To find the cube root of 64, we need to determine which number, when cubed, equals 64. We can test small integers to find the answer. We know that 1\u00b3 = 1 \u00d7 1 \u00d7 1 = 1. Moving to the next integer, 2\u00b3 = 2 \u00d7 2 \u00d7 2 = 8. Then, 3\u00b3 = 3 \u00d7 3 \u00d7 3 = 27. Let’s try 4. Calculating 4\u00b3 means we multiply 4 \u00d7 4 \u00d7 4. The first two fours multiply to 16 (4 \u00d7 4 = 16), and then we multiply that result by the final 4 (16 \u00d7 4 = 64). Since 4\u00b3 is equal to 64, the cube root of 64 is 4.<\/p>\n\n\n\n
b. \u00b3\u221a125<\/strong>
For this part, we are looking for the number that, when multiplied by itself three times, gives 125. We can continue our testing from the previous problem. We already know that 4\u00b3 is 64, so the answer must be a larger number. Let’s test the next integer, 5. To find 5\u00b3, we calculate 5 \u00d7 5 \u00d7 5. The product of the first two fives is 25 (5 \u00d7 5 = 25). Then, we multiply this by the third 5 (25 \u00d7 5 = 125). Because 5\u00b3 equals 125, the cube root of 125 is 5.<\/p>\n\n\n\n
c. \u00b3\u221a-8<\/strong>
This part involves finding the cube root of a negative number. The concept remains the same: we need a number ‘x’ such that x\u00b3 = -8. A positive number cubed always results in a positive number, so the answer must be negative. A negative number multiplied by itself an odd number of times will produce a negative result. For example, (-a) \u00d7 (-a) \u00d7 (-a) = a\u00b2 \u00d7 (-a) = -a\u00b3. Let’s test small negative integers. We can start with -1, where (-1)\u00b3 = -1. Let’s try -2. The calculation is (-2) \u00d7 (-2) \u00d7 (-2). The first part of the multiplication, (-2) \u00d7 (-2), results in a positive 4. We then multiply this 4 by the remaining -2, which gives us -8. Since (-2)\u00b3 equals -8, the cube root of -8 is -2.<\/p>\n\n\n\n
\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
The solution to the equation x3=64 is called the cube root of 64 The Correct Answer and Explanation is: Here are the correct answers to the expressions: a. 4b. 5c. -2 Explanation The problem asks us to evaluate several cube roots based on the provided definition. A cube root of a number is a special value that, […]<\/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-248696","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248696","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=248696"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248696\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}