# How do you rationalize the denominator and simplify 5/sqrt5?

Mar 18, 2016

The answer is $\sqrt{5}$

#### Explanation:

To rationalize a fraction where the denominator is a surd, you must multiply both the numerator and the denominator by the surd denominator of the original fraction.
So $\frac{5}{\sqrt{5}}$ is multiplied by $\frac{\sqrt{5}}{\sqrt{5}}$ which keeps
its value the same as $\frac{\sqrt{5}}{\sqrt{5}}$=1
This gives you $\frac{5 \sqrt{5}}{\sqrt{5} \sqrt{5}}$
which is $\frac{5 \sqrt{5}}{5}$
and this simplifies to $\sqrt{5}$