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: 20

Answer

$\sqrt[3]{\dfrac{7}{10}}=\dfrac{\sqrt[3]{700}}{10}$

Work Step by Step

$\sqrt[3]{\dfrac{7}{10}}$ Rewrite the expression as $\dfrac{\sqrt[3]{7}}{\sqrt[3]{10}}$: $\sqrt[3]{\dfrac{7}{10}}=\dfrac{\sqrt[3]{7}}{\sqrt[3]{10}}=...$ Multiply the fraction by $\dfrac{\sqrt[3]{10^{2}}}{\sqrt[3]{10^{2}}}$ and simplify: $...=\dfrac{\sqrt[3]{7}}{\sqrt[3]{10}}\cdot\dfrac{\sqrt[3]{10^{2}}}{\sqrt[3]{10^{2}}}=\dfrac{\sqrt[3]{7\cdot10^{2}}}{\sqrt[3]{10^{3}}}=\dfrac{\sqrt[3]{700}}{10}$
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