Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 42

Answer

$6\sqrt[]{10}-12\sqrt[]{15}$

Work Step by Step

Using the Distributive Property and the properties of radicals, the given expression, $ 3\sqrt[]{5}(\sqrt[]{8}-2\sqrt[]{12}) ,$ simplifies to \begin{array}{l}\require{cancel} 3\sqrt[]{5}(\sqrt[]{8})-3\sqrt[]{5}(2\sqrt[]{12}) \\\\= 3\sqrt[]{5(8)}-3(2)\sqrt[]{5(12)} \\\\= 3\sqrt[]{40}-6\sqrt[]{60} \\\\= 3\sqrt[]{4\cdot10}-6\sqrt[]{4\cdot15} \\\\= 3\sqrt[]{(2)^2\cdot10}-6\sqrt[]{(2)^2\cdot15} \\\\= 3\cdot2\sqrt[]{10}-6\cdot2\sqrt[]{15} \\\\= 6\sqrt[]{10}-12\sqrt[]{15} .\end{array}
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