Elementary Algebra

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

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 27

Answer

$6\sqrt[]{2}-4\sqrt[]{6}$

Work Step by Step

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ \sqrt[]{12}(\sqrt[]{6}-\sqrt[]{8}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{12}(\sqrt[]{6})-\sqrt[]{12}(\sqrt[]{8}) \\\\= \sqrt[]{12(6)}-\sqrt[]{12(8)} \\\\= \sqrt[]{(2\cdot6)(6)}-\sqrt[]{(4\cdot3)(4\cdot2)} \\\\= \sqrt[]{6^2\cdot2}-\sqrt[]{4^2\cdot6} \\\\= 6\sqrt[]{2}-4\sqrt[]{6} .\end{array}
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