{"id":52,"date":"2023-06-21T13:22:28","date_gmt":"2023-06-21T13:22:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-radicals-and-rational-exponents\/"},"modified":"2023-06-21T13:22:28","modified_gmt":"2023-06-21T13:22:28","slug":"summary-radicals-and-rational-exponents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-radicals-and-rational-exponents\/","title":{"raw":"Summary: Radicals and Rational Exponents","rendered":"Summary: Radicals and Rational Exponents"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\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>\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>\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>\n \t<li>We can add and subtract radical expressions if they have the same radicand and the same index.<\/li>\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>\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>\n \t<li>Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals.<\/li>\n \t<li>The properties of exponents apply to rational exponents.<\/li>\n<\/ul>\n<div>\n<h2>Glossary<\/h2>\n<strong>index<\/strong> the number above the radical sign indicating the <em>n<\/em>th root\n\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]\n\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]\n\n<strong>radical<\/strong> the symbol used to indicate a root\n\n<strong>radical expression<\/strong> an expression containing a radical symbol\n\n<strong>radicand<\/strong> the number under the radical symbol\n\n<\/div>\n\n","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<\/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-52\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><\/ul><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":395986,"menu_order":21,"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\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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