Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 550: 66


$\displaystyle \frac{5\sqrt{5y}}{xy}$

Work Step by Step

Simpify the denominator using $\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab},\qquad$ and $\sqrt[n]{a^{n}}=(\sqrt[n]{a})^{n}=a$ (for positive a). $\sqrt{5x^{2}y}=\sqrt{x^{2}\times 5y}=\sqrt{x^{2}}\times\sqrt{5y} = x\sqrt{5y}$ $... =\displaystyle \frac{25}{x\sqrt{5y}}$ $\displaystyle \color{red}{ \cdot\frac{\sqrt{5y}}{\sqrt{5y}} }\qquad$ (rationalize) $=\displaystyle \frac{25\sqrt{5y}}{x(\sqrt{5y})^{2}}$ $=\displaystyle \frac{25\sqrt{5y}}{x(5y)}$ $\qquad$ ... reduce 5, the common factor = $\displaystyle \frac{5\sqrt{5y}}{xy}$
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