Which choices are real numbers? Check all that apply.
A. (-16)^1\/4
B. (-4)^1\/2
C. (-32)^1\/5
D. (-8)^1\/3<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: C and D<\/strong><\/p>\n\n\n\n To determine which choices are real numbers, we must evaluate the expressions using the rules of exponents and how they apply to negative bases.<\/p>\n\n\n\n This represents the fourth root of (-16). In the set of real numbers, we cannot take an even root (like a square root or fourth root) of a negative number because it does not yield a real number. The result of ((-16)^{1\/4}) would be complex. This represents the square root of (-4). Like in Option A, taking an even root (in this case, a square root) of a negative number results in an imaginary number, not a real number. The square root of (-4) is (2i), where (i) is the imaginary unit. This represents the fifth root of (-32). Odd roots (like the cube root or fifth root) of negative numbers are allowed in the real number system because the result is a real number. For instance, the fifth root of (-32) is (-2), since ((-2)^5 = -32). This represents the cube root of (-8). Like in Option C, the cube root of a negative number results in a real number. The cube root of (-8) is (-2), since ((-2)^3 = -8). The real numbers are C and D<\/strong>, because both involve taking odd roots of negative numbers, which yield real results.<\/p>\n","protected":false},"excerpt":{"rendered":" Which choices are real numbers? Check all that apply.A. (-16)^1\/4B. (-4)^1\/2C. (-32)^1\/5D. (-8)^1\/3 The Correct Answer and Explanation is : The correct answer is: C and D To determine which choices are real numbers, we must evaluate the expressions using the rules of exponents and how they apply to negative bases. Option A: ((-16)^{1\/4}) This […]<\/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-149612","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149612","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=149612"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149612\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Option A: ((-16)^{1\/4})<\/h3>\n\n\n\n
Thus, Option A is not a real number.<\/strong><\/p>\n\n\n\nOption B: ((-4)^{1\/2})<\/h3>\n\n\n\n
Thus, Option B is not a real number.<\/strong><\/p>\n\n\n\nOption C: ((-32)^{1\/5})<\/h3>\n\n\n\n
Thus, Option C is a real number.<\/strong><\/p>\n\n\n\nOption D: ((-8)^{1\/3})<\/h3>\n\n\n\n
Thus, Option D is a real number.<\/strong><\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n