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: 26


$\frac{y\sqrt z}{6}$

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, $\sqrt (\frac{y^{2}z}{36})=\frac{\sqrt (y^{2}z)}{\sqrt 36}=\frac{\sqrt (y^{2})\times\sqrt z}{\sqrt 36}=\frac{y\sqrt z}{6}$ We know that $\sqrt (y^{2})=y$, because $(y)^{2}=y^{2}$. Also, we know that $\sqrt 36=6$, because $6^{2}=36$.
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