Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 434: 115


$\frac{\sqrt[3] 64}{\sqrt 64}=\frac{4}{8}=\frac{1}{2}$

Work Step by Step

We are given that $\frac{\sqrt[3] 64}{\sqrt 64}=\sqrt[3] \frac{64}{64}=\sqrt[3] 1=1$. This simplification incorrectly uses the quotient rule. In general, we can only use the quotient rule when both radicals have the same index. In this case, we must simplify without using the quotient rule, since each radical has a different index. $\frac{\sqrt[3] 64}{\sqrt 64}=\frac{4}{8}=\frac{1}{2}$ We know that $\sqrt[3] 64=4$, because $4^{3}=64$. We also know that $\sqrt 64=8$, because $8^{2}=64$.
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