Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 39

Answer

$\frac{\sqrt[3] (r^{2})}{2}$

Work Step by Step

The quotient rule for radicals tells us that $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (if $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots. Therefore, $\sqrt[3] \frac{r^{2}}{8}=\frac{\sqrt[3] (r^{2})}{\sqrt[3] 8}=\frac{\sqrt[3] (r^{2})}{2}$. $\sqrt[3] 8=2$, because $2^{3}=8$
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