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: 57

Answer

$\sqrt[3]{\dfrac{7}{8}}=\dfrac{7}{2\sqrt[3]{49}}$

Work Step by Step

$\sqrt[3]{\dfrac{7}{8}}$ Rewrite this expression as $\dfrac{\sqrt[3]{7}}{\sqrt[3]{8}}$ and simplify it: $\sqrt[3]{\dfrac{7}{8}}=\dfrac{\sqrt[3]{7}}{\sqrt[3]{8}}=\dfrac{\sqrt[3]{7}}{2}=...$ Multiply this fraction by $\dfrac{\sqrt[3]{49}}{\sqrt[3]{49}}$ and simplify again if possible: $...=\dfrac{\sqrt[3]{7}}{2}\cdot\dfrac{\sqrt[3]{49}}{\sqrt[3]{49}}=\dfrac{\sqrt[3]{343}}{2\sqrt[3]{49}}=\dfrac{7}{2\sqrt[3]{49}}$
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