Answer
$\displaystyle \sqrt{\frac{9}{8}}=\frac{3}{2\sqrt{2}}$
Work Step by Step
$\sqrt{\frac{9}{8}}\qquad$ ...apply the Quotient Property:$\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
$=\displaystyle \frac{\sqrt{9}}{\sqrt{8}}\qquad$ ...evaluate the numerator ($\sqrt{9}=3$) and write $8$ as $4\cdot 2$.
$=\displaystyle \frac{3}{\sqrt{4.2}}\qquad$ ...use the Product Property of square roots in the denominator:$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$
$=\displaystyle \frac{3}{\sqrt{4}\cdot\sqrt{2}}\qquad$ ...evaluate part of the denominator ($\sqrt{4}=2$).
$=\displaystyle \frac{3}{2\sqrt{2}}$
