Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 60

Answer

$\sqrt[3]{\dfrac{9y}{7}}=\dfrac{3y}{\sqrt[3]{21y^{2}}}$

Work Step by Step

$\sqrt[3]{\dfrac{9y}{7}}$ Rewrite this expression as $\dfrac{\sqrt[3]{9y}}{\sqrt[3]{7}}$: $\sqrt[3]{\dfrac{9y}{7}}=\dfrac{\sqrt[3]{9y}}{\sqrt[3]{7}}=...$ Multiply this fraction by $\dfrac{\sqrt[3]{3y^{2}}}{\sqrt[3]{3y^{2}}}$ and simplify if possible: $...=\dfrac{\sqrt[3]{9y}}{\sqrt[3]{7}}\cdot\dfrac{\sqrt[3]{3y^{2}}}{\sqrt[3]{3y^{2}}}=\dfrac{\sqrt[3]{27y^{3}}}{\sqrt[3]{21y^{2}}}=\dfrac{3y}{\sqrt[3]{21y^{2}}}$
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