Answer
$\frac{\sqrt 3}{2}$
Preference and explanation may vary.
Work Step by Step
To simplify $\frac{3}{\sqrt {12}}$, here is one way:
$\frac{3}{\sqrt {12}}$ = $\frac{3}{\sqrt 4\sqrt 3}$ = $\frac{3}{2\sqrt 3}$
Rationalize the denominator:
$\frac{3}{2\sqrt 3}$$\times$$\frac{\sqrt 3}{\sqrt 3}$ = $\frac{3\sqrt 3}{2(3)}$ = $\frac{\sqrt 3}{2}$
Here's another way:
$\frac{3}{\sqrt {12}}$$\times$$\frac{\sqrt {12}}{\sqrt {12}}$ = $\frac{3\sqrt {12}}{12}$ = $\frac{3\sqrt 4\sqrt 3}{12}$ = $\frac{3\times2\sqrt 3}{12}$ = $\frac{6\sqrt 3}{12}$ = $\frac{\sqrt 3}{2}$
Preference and explanation of preference of method vary by student.
