# How do do you rationalize the square root of 5 divided by the square root of 8?

Sep 8, 2015

sqrt5/sqrt8 = color(green)(sqrt10/4

#### Explanation:

Rationalisation is simply expressing a fraction in a form that has a rational denominator .

$\frac{\sqrt{5}}{\sqrt{8}}$ is the fraction that we have been given

The denominator $\sqrt{8}$ is irrational. To convert it to a rational number, we can multiply the numerator and the denominator of the fraction by $\sqrt{2}$

$\frac{\sqrt{5}}{\sqrt{8}} = \frac{\sqrt{5} \cdot \sqrt{2}}{\sqrt{8} \cdot \sqrt{2}}$

We know that color(blue)(sqrta*sqrtb = sqrt(ab)
Hence$\frac{\sqrt{5} \cdot \sqrt{2}}{\sqrt{8} \cdot \sqrt{2}} = \frac{\sqrt{5 \cdot 2}}{\sqrt{8 \cdot 2}} = \frac{\sqrt{10}}{\sqrt{16}} = \frac{\sqrt{10}}{4}$

Now the denominator 4 is rational. Hence we can be sure that we have rationalised the denominator

sqrt5/sqrt8 = color(green)(sqrt10/4