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 - Page 717: 19



Work Step by Step

$\sqrt[3]{\dfrac{3}{5}}$ Rewrite this expression as $\dfrac{\sqrt[3]{3}}{\sqrt[3]{5}}$: $\sqrt[3]{\dfrac{3}{5}}=\dfrac{\sqrt[3]{3}}{\sqrt[3]{5}}=...$ Multiply the fraction by $\dfrac{\sqrt[3]{5^{2}}}{\sqrt[3]{5^{2}}}$ and simplify: $...=\dfrac{\sqrt[3]{3}}{\sqrt[3]{5}}\cdot\dfrac{\sqrt[3]{5^{2}}}{\sqrt[3]{5^{2}}}=\dfrac{\sqrt[3]{3\cdot25}}{\sqrt[3]{5^{3}}}=\dfrac{\sqrt[3]{75}}{5}$
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