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: 27

Answer

$\frac{x\sqrt 5}{2y}$

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, $\sqrt (\frac{5x^{2}}{4y^{2}})=\frac{\sqrt (5x^{2})}{\sqrt (4y^{2})}=\frac{\sqrt (x^{2})\times\sqrt 5}{\sqrt (4y^{2})}=\frac{x\sqrt 5}{2y}$ We know that $\sqrt (4y^{2})=2y$, because $(2y)^{2}=(2\times2)\times y^{1+1}=4y^{2}$. Also, we know that $\sqrt (x^{2})=x$, because $(x)^{2}=x^{2}$.
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