## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - Chapter 9 Test - Page 431: 17

#### Answer

$12\sqrt[]{2}-12\sqrt{3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[]{6}(2\sqrt[]{12}-3\sqrt{8}) ,$ simplifies to \begin{array}{l}\require{cancel} 2\sqrt[]{6(12)}-3\sqrt{6(8}) \\\\= 2\sqrt[]{6(6\cdot2)}-3\sqrt{(2\cdot3)(8}) \\\\= 2\sqrt[]{(6)^2\cdot2}-3\sqrt{16\cdot3} \\\\= 2\cdot6\sqrt[]{2}-3\sqrt{(4)^2\cdot3} \\\\= 2\cdot6\sqrt[]{2}-3(4)\sqrt{3} \\\\= 12\sqrt[]{2}-12\sqrt{3} .\end{array}

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