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: 58

Answer

$\sqrt[3]{\dfrac{25}{2}}=\dfrac{5}{\sqrt[3]{10}}$

Work Step by Step

$\sqrt[3]{\dfrac{25}{2}}$ Rewrite this expression as $\dfrac{\sqrt[3]{25}}{\sqrt[3]{2}}$: $\sqrt[3]{\dfrac{25}{2}}=\dfrac{\sqrt[3]{25}}{\sqrt[3]{2}}=...$ Multiply this fraction by $\dfrac{\sqrt[3]{5}}{\sqrt[3]{5}}$ and simplify if possible: $...=\dfrac{\sqrt[3]{25}}{\sqrt[3]{2}}\cdot\dfrac{\sqrt[3]{5}}{\sqrt[3]{5}}=\dfrac{\sqrt[3]{125}}{\sqrt[3]{10}}=\dfrac{5}{\sqrt[3]{10}}$
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