# How do you simplify (7sqrt3)/(3-sqrt2)?

##### 1 Answer
Jul 28, 2016

I found: $3 \sqrt{3} + \sqrt{6}$

#### Explanation:

We can try Rationalizing by multiplying and dividing by: $3 + \sqrt{2}$ to get:
$\frac{7 \sqrt{3}}{3 - \sqrt{2}} \cdot \frac{3 + \sqrt{2}}{3 + \sqrt{2}} =$
$= \frac{21 \sqrt{3} + 7 \sqrt{3} \sqrt{2}}{9 + \cancel{3 \sqrt{2}} \cancel{- 3 \sqrt{2}} - 2} =$
$= \frac{21 \sqrt{3} + 7 \sqrt{6}}{7} =$
$= \frac{21}{7} \sqrt{3} + \frac{7}{7} \sqrt{6} = 3 \sqrt{3} + \sqrt{6}$