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: 56

Answer

$-\dfrac{17\sqrt{6}}{3}$

Work Step by Step

Using the properties of radicals, the given expression, $ \sqrt{\dfrac{2}{3}}-2\sqrt{54} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{2}{3}\cdot\dfrac{3}{3}}-2\sqrt{9\cdot6} \\\\= \sqrt{\dfrac{6}{9}}-2\sqrt{(3)^2\cdot6} \\\\= \dfrac{\sqrt{6}}{\sqrt{9}}-2\cdot3\sqrt{6} \\\\= \dfrac{\sqrt{6}}{\sqrt{(3)^2}}-6\sqrt{6} \\\\= \dfrac{\sqrt{6}}{3}-6\sqrt{6} \\\\= \dfrac{\sqrt{6}}{3}-\dfrac{18}{3}\sqrt{6} \\\\= -\dfrac{17\sqrt{6}}{3} .\end{array}
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