Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapter 9 Test: 20

Answer

$4\sqrt{6}$

Work Step by Step

Using the properties of equality, the given expression, $ 2\sqrt{24}-4\sqrt{54}+3\sqrt{96} ,$ simplifies to \begin{array}{l}\require{cancel} 2\sqrt{4\cdot6}-4\sqrt{9\cdot6}+3\sqrt{16\cdot6} \\\\= 2\sqrt{(2)^2\cdot6}-4\sqrt{(3)^2\cdot6}+3\sqrt{(4)^2\cdot6} \\\\= 2(2)\sqrt{6}-4(3)\sqrt{6}+3(4)\sqrt{6} \\\\= 4\sqrt{6}-12\sqrt{6}+12\sqrt{6} \\\\= 4\sqrt{6} .\end{array}
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