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 - Page 430: 29

Answer

$4y\sqrt[]{3x}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{4}{3}\sqrt[]{27xy^2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4}{3}\sqrt[]{9y^2\cdot3x} \\\\= \dfrac{4}{3}\sqrt[]{(3y)^2\cdot3x} \\\\= \dfrac{4}{3}\cdot3y\sqrt[]{3x} \\\\= \dfrac{4}{\cancel{3}}\cdot\cancel{3}y\sqrt[]{3x} \\\\= 4y\sqrt[]{3x} .\end{array} Note that all variables are assumed to have positive values.
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