# How do you simplify 5/sqrt5?

Apr 12, 2017

$\sqrt{5}$

#### Explanation:

Whenever you have a surd as the denominator, we rationalise it, meaning we multiply it and the numerator (because multiplying any number by 1 doesn't change it) by itself to get a 'normal' number on the bottom. So in this case we would do

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

*notice how $\frac{\sqrt{5}}{\sqrt{5}} = 1$ so by multiplying $\frac{5}{\sqrt{5}}$ we are to changing it *

Then we would simplify $\frac{5 \sqrt{5}}{5}$ to get $\frac{1 \sqrt{5}}{1}$ which equals to $\sqrt{5}$

Apr 13, 2017

$\sqrt{5}$

#### Explanation:

color(blue)(5/sqrt(5)

We need to simplify this.The first thing we need to know is that, we need to rationalize the denominator.

So, multiply the denominator and numerator with $\sqrt{5}$

$\rightarrow \frac{5}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

$\rightarrow \frac{5 \sqrt{5}}{5}$

$\rightarrow \frac{\cancel{5} \sqrt{5}}{\cancel{5}}$

color(green)(rArrsqrt5

Hope this helps... :)