# How do you rationalize the denominator and simplify sqrt36/sqrt8?

Apr 7, 2016

$\frac{\sqrt{36}}{\sqrt{8}} = \frac{3 \sqrt{2}}{2}$

#### Explanation:

To rationalize the denominator in $\frac{\sqrt{36}}{\sqrt{8}}$, let us examine the denominator.

As $\sqrt{8} = \sqrt{2 \times 2 \times 2} = 2 \sqrt{2}$, if we multiply this by $\sqrt{2}$, it will become rational.

Hence multiplying numerator and denominator by$\sqrt{2}$ we get

$\frac{\sqrt{36}}{\sqrt{8}} = \frac{\sqrt{36} \times \sqrt{2}}{\sqrt{8} \times \sqrt{2}}$

= $\frac{6 \sqrt{2}}{\sqrt{16}} = \frac{6 \sqrt{2}}{4} = \frac{3 \cancel{6} \sqrt{2}}{2 \cancel{4}} = \frac{3 \sqrt{2}}{2}$