{"id":275,"date":"2015-09-18T20:29:49","date_gmt":"2015-09-18T20:29:49","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=275"},"modified":"2015-11-03T18:59:00","modified_gmt":"2015-11-03T18:59:00","slug":"key-concepts-glossary-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/key-concepts-glossary-3\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n\t<li>The principal square root of a number [latex]a[\/latex] is the nonnegative number that when multiplied by itself equals [latex]a[\/latex].<\/li>\r\n\t<li>If [latex]a[\/latex] and [latex]b[\/latex] are nonnegative, the square root of the product [latex]ab[\/latex] is equal to the product of the square roots of [latex]a[\/latex] and [latex]b[\/latex]<\/li>\r\n\t<li>If [latex]a[\/latex] and [latex]b[\/latex] are nonnegative, the square root of the quotient [latex]\\frac{a}{b}[\/latex] is equal to the quotient of the square roots of [latex]a[\/latex] and [latex]b[\/latex]<\/li>\r\n\t<li>We can add and subtract radical expressions if they have the same radicand and the same index.<\/li>\r\n\t<li>Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.<\/li>\r\n\t<li>The principal <em>n<\/em>th root of [latex]a[\/latex] is the number with the same sign as [latex]a[\/latex] that when raised to the <em>n<\/em>th power equals [latex]a[\/latex]. These roots have the same properties as square roots.<\/li>\r\n\t<li>Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals.<\/li>\r\n\t<li>The properties of exponents apply to rational exponents.<\/li>\r\n<\/ul>\r\n<div>\r\n<h2>Glossary<\/h2>\r\n<strong>index<\/strong> the number above the radical sign indicating the <em>n<\/em>th root\r\n\r\n<strong>principal <em>n<\/em>th root<\/strong> the number with the same sign as [latex]a[\/latex] that when raised to the <em>n<\/em>th power equals [latex]a[\/latex]\r\n\r\n<strong>principal square root<\/strong> the nonnegative square root of a number [latex]a[\/latex] that, when multiplied by itself, equals [latex]a[\/latex]\r\n\r\n<strong>radical<\/strong> the symbol used to indicate a root\r\n\r\n<strong>radical expression<\/strong> an expression containing a radical symbol\r\n\r\n<strong>radicand<\/strong> the number under the radical symbol\r\n\r\n&nbsp;\r\n\r\n<\/div>","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>The principal square root of a number [latex]a[\/latex] is the nonnegative number that when multiplied by itself equals [latex]a[\/latex].<\/li>\n<li>If [latex]a[\/latex] and [latex]b[\/latex] are nonnegative, the square root of the product [latex]ab[\/latex] is equal to the product of the square roots of [latex]a[\/latex] and [latex]b[\/latex]<\/li>\n<li>If [latex]a[\/latex] and [latex]b[\/latex] are nonnegative, the square root of the quotient [latex]\\frac{a}{b}[\/latex] is equal to the quotient of the square roots of [latex]a[\/latex] and [latex]b[\/latex]<\/li>\n<li>We can add and subtract radical expressions if they have the same radicand and the same index.<\/li>\n<li>Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.<\/li>\n<li>The principal <em>n<\/em>th root of [latex]a[\/latex] is the number with the same sign as [latex]a[\/latex] that when raised to the <em>n<\/em>th power equals [latex]a[\/latex]. These roots have the same properties as square roots.<\/li>\n<li>Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals.<\/li>\n<li>The properties of exponents apply to rational exponents.<\/li>\n<\/ul>\n<div>\n<h2>Glossary<\/h2>\n<p><strong>index<\/strong> the number above the radical sign indicating the <em>n<\/em>th root<\/p>\n<p><strong>principal <em>n<\/em>th root<\/strong> the number with the same sign as [latex]a[\/latex] that when raised to the <em>n<\/em>th power equals [latex]a[\/latex]<\/p>\n<p><strong>principal square root<\/strong> the nonnegative square root of a number [latex]a[\/latex] that, when multiplied by itself, equals [latex]a[\/latex]<\/p>\n<p><strong>radical<\/strong> the symbol used to indicate a root<\/p>\n<p><strong>radical expression<\/strong> an expression containing a radical symbol<\/p>\n<p><strong>radicand<\/strong> the number under the radical symbol<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-275\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-275","chapter","type-chapter","status-publish","hentry"],"part":203,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/275","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/275\/revisions"}],"predecessor-version":[{"id":543,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/275\/revisions\/543"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/203"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/275\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=275"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=275"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=275"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}