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: 94


$\displaystyle \frac{5}{\sqrt{15}}$

Work Step by Step

$\displaystyle \sqrt{\frac{5}{3}}=\frac{\sqrt{5}}{\sqrt{3}}$ We are rationalizing the numerator, using $\sqrt[n]{a^{n}}=(\sqrt[n]{a})^{n}=a \qquad$(for positive a) and $\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab}$ $=\displaystyle \frac{\sqrt{5}}{\sqrt{3}}\color{red}{ \cdot\frac{\sqrt{5}}{\sqrt{5}} }\qquad$ (rationalize) $=\displaystyle \frac{5}{\sqrt{15}}$
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