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: 25

Answer

$\frac{x\sqrt y}{10}$

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, $\sqrt (\frac{x^{2}y}{100})=\frac{\sqrt (x^{2}y)}{\sqrt 100}=\frac{\sqrt (x^{2})\times\sqrt y}{\sqrt 100}=\frac{x\sqrt y}{10}$ We know that $\sqrt (x^{2})=x$, because $(x)^{2}=x^{2}$. Also, we know that $\sqrt 100=10$, because $10^{2}=100$.
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