{"id":4793,"date":"2012-11-05T21:49:53","date_gmt":"2012-11-05T21:49:53","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4793"},"modified":"2014-12-02T08:31:57","modified_gmt":"2014-12-02T08:31:57","slug":"cubes-and-cube-roots","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/cubes-and-cube-roots\/","title":{"rendered":"Cubes and Cube Roots"},"content":{"rendered":"<p><strong>Cube:<\/strong><\/p>\n<p>The cube of a number <strong><em>a <\/em><\/strong>is denoted by <strong><em>a<sup>3<\/sup><\/em><\/strong> and it is nothing but the product of <strong><em>a<\/em><\/strong> for 3 rimes.<\/p>\n<p>So, a<sup>3<\/sup> = a x a x a<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4794\" title=\"cube root1\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root1.jpg\" alt=\"\" width=\"460\" height=\"190\" srcset=\"https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root1.jpg 460w, https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root1-300x123.jpg 300w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/a><\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>2<sup>3<\/sup> = 2x2x2 = 8<\/p>\n<p>5<sup>3 <\/sup>= 5x5x5 = 125<\/p>\n<p><strong>Note:<\/strong><\/p>\n<p>(1)\u00a0\u00a0\u00a0 If a<sup>3<\/sup> =b then the unit digit of all numbers ending with <strong><em>a<\/em><\/strong> is <strong><em>b.<\/em><\/strong><\/p>\n<p>(2)\u00a0\u00a0\u00a0 The sum of <strong><em>n <\/em><\/strong>natural odd numbers is<strong><em> n<sup>3<\/sup><\/em><\/strong>.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4795\" title=\"cube root2\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root2.jpg\" alt=\"\" width=\"369\" height=\"173\" srcset=\"https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root2.jpg 369w, https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root2-300x140.jpg 300w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/a><\/p>\n<p><strong>(3)\u00a0\u00a0\u00a0 <\/strong>If a given number is a <strong>perfect cube<\/strong>, then its <strong>prime factors<\/strong> will always occur in <strong>groups of three.<\/strong><strong><\/strong><\/p>\n<p><strong>Cube root:<\/strong><\/p>\n<p>Cube root is the other way of cube. <strong><em>a<\/em><\/strong> is called the cube root of <strong><em>b <\/em><\/strong>if a<strong><em><sup>3<\/sup><\/em><\/strong> =b.<\/p>\n<p>i.e. if 3<sup>3<\/sup> =27 then 3 is called cube root of 27.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4796\" title=\"cube root3\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root3.jpg\" alt=\"\" width=\"342\" height=\"92\" srcset=\"https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root3.jpg 342w, https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root3-300x80.jpg 300w\" sizes=\"auto, (max-width: 342px) 100vw, 342px\" \/><\/a><\/p>\n<p>So, the cube root of a number is a number which when cubed gives the original number. The cube root is denoted by the symbol <a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root4.jpg\"><img loading=\"lazy\" decoding=\"async\" title=\"cube root4\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root4.jpg\" alt=\"\" width=\"28\" height=\"45\" \/><\/a>.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root51.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4800\" title=\"cube root5\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/cube-root51.jpg\" alt=\"\" width=\"97\" height=\"45\" \/><\/a><\/p>\n<p>The cube root of a number can be found using estimating or prime factorization method.<\/p>\n<p>Do you also need help with Geography? Take a look at our <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/private-tutoring\/\">Geography tutoring services.<\/a> <\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Prince-Edward-Island visit: <a href=\"https:\/\/schooltutoring.com\/Prince-Edward-Island-Tutoring-Programs\/\">Tutoring in Prince-Edward-Island. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cube: The cube of a number a is denoted by a3 and it is nothing but the product of a for 3 rimes. So, a3 = a x a x a Example: 23 = 2x2x2 = 8 53 = 5x5x5 = 125 Note: (1)\u00a0\u00a0\u00a0 If a3 =b then the unit digit of all numbers ending [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[438,1179,1223,1558,1774],"class_list":["post-4793","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-cube","tag-natural","tag-numbers","tag-root","tag-sum"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4793","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=4793"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4793\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4793"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4793"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}