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 433: 114



Work Step by Step

The quotient rule states that $\frac{\sqrt[n] a}{\sqrt[n] b}=\sqrt[n] (\frac{a}{b})$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero). Therefore, $\frac{\sqrt[3] 12}{\sqrt[3] 4}=\sqrt[3] 8$ is a false statement. The correct statement is $\frac{\sqrt[3] 12}{\sqrt[3] 4}=\sqrt[3] \frac{12}{4}=\sqrt[3] 3$.
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