# How do you rationalize the denominator and simplify sqrt (1 / 3)?

Dec 23, 2016

$\sqrt{\frac{1}{3}} = \frac{\sqrt{3}}{3}$

#### Explanation:

If $a , b > 0$ then $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

So we find:

$\sqrt{\frac{1}{3}} = \sqrt{\frac{3}{9}} = \sqrt{\frac{3}{3} ^ 2} = \frac{\sqrt{3}}{\sqrt{{3}^{2}}} = \frac{\sqrt{3}}{3}$

The trick is to make the denominator of a fraction into a perfect square before you take the square root.