Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapter 9 Test - Page 431: 18



Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the Distributive Property, and the properties of radicals, the given expression, $ (2\sqrt[]{5}+\sqrt{3})(\sqrt[]{5}-3\sqrt{3}) ,$ simplifies to \begin{array}{l}\require{cancel} 2\sqrt[]{5}(\sqrt[]{5})+2\sqrt[]{5}(-3\sqrt{3})+\sqrt{3}(\sqrt[]{5})+\sqrt{3}(-3\sqrt{3}) \\\\= 2(\sqrt[]{5^{2}})-2(3)\sqrt[]{5(3)}+\sqrt{3(5)}-3(\sqrt{3^{2}}) \\\\= 2(5)-6\sqrt[]{15}+\sqrt{15}-3(3) \\\\= 10-6\sqrt[]{15}+\sqrt{15}-9 \\\\= (10-9)+(-6\sqrt[]{15}+\sqrt{15}) \\\\= 1-5\sqrt[]{15} .\end{array}
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