# How do you divide (8sqrt6)/(2sqrt3)?

Mar 4, 2018

$4 \sqrt{2}$

#### Explanation:

We must use our knowledge of surds:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$\implies \sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3}$

$\frac{8 \sqrt{6}}{2 \sqrt{3}} = \frac{8 \sqrt{2} \cdot \sqrt{3}}{2 \sqrt{3}}$

We can cancel out the $\sqrt{3}$ as on both numerator and denominator:

$\frac{8 \sqrt{2} \cdot \cancel{\sqrt{3}}}{2 \cancel{\sqrt{3}}} = \frac{8 \sqrt{2}}{2}$

We know $\frac{8}{2} = 4$

$\implies 4 \sqrt{2}$