# How do you simplify (9+3sqrt6) /sqrt3?

Feb 18, 2016

$3 \sqrt{3} + 3 \sqrt{2}$

#### Explanation:

To simplify $\frac{9 + 3 \sqrt{6}}{\sqrt{3}}$, we have to first rationalize denominator. Here as denominator is pure irrational number $\sqrt{3}$, we multiply numerator and denominator both by $\sqrt{3}$.

The fraction than becomes

$\left(\frac{9 + 3 \sqrt{6}}{\sqrt{3}}\right) \cdot \frac{\sqrt{3}}{\sqrt{3}}$ or

$\frac{9 \sqrt{3} + 3 \sqrt{6} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}$, which simplifies to

$\frac{9 \sqrt{3} + 3 \sqrt{18}}{3}$ or $\frac{9 \sqrt{3} + 3 \cdot 3 \sqrt{2}}{3}$ or

$3 \sqrt{3} + 3 \sqrt{2}$