Answer
$\displaystyle \frac{7}{\sqrt{12}}=\frac{7\sqrt{3}}{6}$
Work Step by Step
$\displaystyle \frac{7}{\sqrt{12}}\qquad$ ...using the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ , rewrite $\sqrt{12}$ as $\sqrt{4\cdot 3}$
$=\displaystyle \frac{7}{\sqrt{4\cdot 3}}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$
$=\displaystyle \frac{7}{\sqrt{4}\cdot\sqrt{3}}\qquad$ ...simplify ($\sqrt{4}=2$)
$=\displaystyle \frac{7}{2\sqrt{3}}\qquad$ ...rationalize the denominator by multyplying both the numerator and the denominator with $\sqrt{3}$.
$=\displaystyle \frac{7\cdot\sqrt{3}}{2\sqrt{3}\cdot\sqrt{3}}\qquad$ ...simplify
$=\displaystyle \frac{7\sqrt{3}}{6}$
