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: 34

Answer

$\dfrac{x\sqrt{2x}}{3}$

Work Step by Step

Using the properties of radicals, the given expression, $ \sqrt{\dfrac{2x^3}{9}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{x^2}{9}\cdot2x} \\\\= \sqrt{\left(\dfrac{x}{3}\right)^2\cdot2x} \\\\= \dfrac{x}{3}\sqrt{2x} \\\\= \dfrac{x\sqrt{2x}}{3} .\end{array} Note that all variables are assumed to have positive values.
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