# How do you simplify 5/sqrt10?

Oct 4, 2016

$\frac{\sqrt{10}}{2}$

#### Explanation:

You have to follow a process called rationalizing when you have a denominator that is an irrational number.

In this process you multiply the numerator and denominator by the irrational number that is in the denominator.

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

This is the same as multiplying by 1, so the look of the ratio but it is still equivalent.

$\frac{\sqrt{10}}{\sqrt{10}}$ is the same as 1.

$\frac{5}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}} = \frac{5 \sqrt{10}}{\sqrt{100}} = \frac{5 \sqrt{10}}{10} = \frac{\cancel{5} \sqrt{10}}{\cancel{5} \cdot 2} = \frac{\sqrt{10}}{2}$

Oct 4, 2016

Always multiply by the surd you want to eliminate ($\sqrt{10}$)

#### Explanation:

$\frac{5}{\sqrt{10}}$=$\frac{5}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$
$= \frac{5 \cdot \sqrt{10}}{10}$
$= \frac{\sqrt{10}}{2}$
$= \frac{\sqrt{2 \cdot 5}}{2}$
$= \frac{1}{2} \sqrt{10}$
$= \frac{1}{2} \sqrt{2} \sqrt{5}$