Answer
$ \displaystyle \frac{3}{\sqrt{6}}$
Work Step by Step
$\displaystyle \sqrt{\frac{3}{2}}=\frac{\sqrt{3}}{\sqrt{2}}$
We are rationalizing the numerator, using
$\sqrt[n]{a^{n}}=(\sqrt[n]{a})^{n}=a \qquad$(for positive a)
and $\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab}$
$=\displaystyle \frac{\sqrt{3}}{\sqrt{2}}\color{red}{ \cdot\frac{\sqrt{3}}{\sqrt{3}} }\qquad$ (rationalize)
$=\displaystyle \frac{3}{\sqrt{6}}$
