# How do you divide (sqrt6+sqrt3)/ sqrt2?

Jun 16, 2015

$\sqrt{3} + \frac{\sqrt{6}}{2}$

#### Explanation:

Separate the numerator using the common denominator of $\sqrt{2}$

$\frac{\sqrt{6}}{\sqrt{2}} + \frac{\sqrt{3}}{\sqrt{2}}$

Write using single radicals, $\sqrt{}$

$\sqrt{\frac{6}{2}} + \frac{\sqrt{3}}{\sqrt{2}}$

Simplify the first term

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

Rationalize the second term by multiplying the numerator and denominator by $\sqrt{2}$

$\sqrt{3} + \frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \sqrt{3} + \frac{\sqrt{6}}{2}$