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 432: 14


$\frac{2\sqrt 2}{9}$

Work Step by Step

The quotient rule holds that $\sqrt[n] (\frac{a}{b})=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero). Therefore, $\sqrt (\frac{8}{81})=\frac{\sqrt 8}{\sqrt 81}=\frac{\sqrt (4\times2)}{\sqrt 81}=\frac{\sqrt 4\times\sqrt 2}{\sqrt 81}=\frac{2\sqrt 2}{9}$ We know that $\sqrt 81=9$, because $9^{2}=81$. Also, we know that $\sqrt 4=2$, because $2^{2}=4$
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