Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Review: 105

Answer

$\dfrac{5\sqrt[3]{2}}{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the denominator of the given expression, $ \dfrac{5}{\sqrt[3]{4}} ,$ multiply by an expression equal to $1$ which will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the given expression by an expression equal to $1$ which will make the denominator a perfect power of the index and then simplifying the radical result to \begin{array}{l}\require{cancel} \dfrac{5}{\sqrt[3]{4}}\cdot\dfrac{\sqrt[3]{2}}{\sqrt[3]{2}} \\\\= \dfrac{5\sqrt[3]{2}}{\sqrt[3]{8}} \\\\= \dfrac{5\sqrt[3]{2}}{\sqrt[3]{(2)^3}} \\\\= \dfrac{5\sqrt[3]{2}}{2} .\end{array}
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