# How do you rationalize the denominator and simplify sqrt(5/10)?

Apr 18, 2016

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

#### Explanation:

First, we can simplify what's in the big root sign:
$\sqrt{\frac{5}{10}} = \sqrt{\frac{1}{2}}$
And we can split the big root sign into two smaller ones:
$= \frac{\sqrt{1}}{\sqrt{2}}$
$= \frac{1}{\sqrt{2}}$
Now we do something unexpected, and put another term into the equation.
$= \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$
We can do this because $\frac{\sqrt{2}}{\sqrt{2}}$ is just 1, and anything times 1 is itself. Moreover we do this because the question asks us to rationalise the denominator, asking to remove any root signs.
$= \frac{\sqrt{2}}{\sqrt{2} \cdot \sqrt{2}}$
$= \frac{\sqrt{2}}{2}$