# How do you rationalize the denominator and simplify sqrt2/sqrt5?

Apr 4, 2016

$\frac{\sqrt{10}}{5}$

#### Explanation:

Multiply by 1 and you do not change the inherent value. 1 can come in many forms. Foe example: $1 = \frac{\sqrt{5}}{\sqrt{5}}$

Multiply by 1 but in the form of $1 = \frac{\sqrt{5}}{\sqrt{5}}$ giving

$\frac{\sqrt{2}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$

$= \frac{\sqrt{2} \sqrt{5}}{5}$

$= \frac{\sqrt{2 \times 5}}{5}$

$\frac{\sqrt{10}}{5}$