# How do you simplify  sqrt (0.5)?

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

#### Explanation:

The difficult part here is dealing with a decimal inside the root sign. So let's change that to a fraction and see if it's easier to deal with:

$\sqrt{.5} = \sqrt{\frac{1}{2}}$

This is good - there is now no decimal inside the root. But now we have to deal with a root in the denominator of our fraction. So let's get rid of it through a creative use of multiplying by 1:

$\sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \left(\frac{1}{\sqrt{2}}\right) \left(1\right) = \left(\frac{1}{\sqrt{2}}\right) \left(\frac{\sqrt{2}}{\sqrt{2}}\right) = \frac{\sqrt{2}}{2}$