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 551: 110



Work Step by Step

$\displaystyle \sqrt{\frac{5}{3}}=\sqrt{\frac{25}{15}}=\frac{\sqrt{25}}{\sqrt{15}}=\frac{5}{\sqrt{15}}\color{red}{ \cdot\frac{ \sqrt{15}}{\sqrt{15}} }= \frac{5\sqrt{15}}{15}=3\sqrt{15}$ $\displaystyle \sqrt{\frac{3}{5}}=\sqrt{\frac{9}{15}}=\frac{\sqrt{9}}{\sqrt{15}}=\frac{3}{\sqrt{15}}\color{red}{ \cdot\frac{ \sqrt{15}}{\sqrt{15}} }=\frac{3\sqrt{15}}{15}$ $\displaystyle \sqrt{15}-\sqrt{\frac{5}{3}}+\sqrt{\frac{3}{5}}= \frac{15\sqrt{15}}{15}-\frac{5\sqrt{15}}{15}+\frac{3\sqrt{15}}{15}\\\\\\=\dfrac{13\sqrt{15}}{15}$
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