How do you simplify 5sqrt3/sqrt12?

Nov 1, 2015

$\frac{5}{2}$

Explanation:

$\left[1\right] \text{ } \frac{5 \sqrt{3}}{\sqrt{12}}$

Rationalize the denominator by multiplying to $\frac{\sqrt{12}}{\sqrt{12}}$.

$\left[2\right] \text{ } = \frac{5 \sqrt{3}}{\sqrt{12}} \cdot \frac{\sqrt{12}}{\sqrt{12}}$

$\left[3\right] \text{ } = \frac{5 \sqrt{36}}{12}$

Get the principal square root of $36$.

$\left[4\right] \text{ } = \frac{5 \left(6\right)}{12}$

$\left[5\right] \text{ } = \frac{30}{12}$

Put in simplest terms.

$\left[6\right] \text{ } = \textcolor{b l u e}{\frac{5}{2}}$