## Intermediate Algebra for College Students (7th Edition)

$\displaystyle \frac{5}{\sqrt{15}}$
$\displaystyle \sqrt{\frac{5}{3}}=\frac{\sqrt{5}}{\sqrt{3}}$ 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) $=\displaystyle \frac{5}{\sqrt{15}}$