# How do you simplify: the square root of 4/9?

Jul 23, 2015

#### Answer:

You take the square root of the denominator and of the numerator.

#### Explanation:

Start by writing out your initial expression

$\sqrt{\frac{4}{9}}$

If you use the quotient property of radicals, you can write this expression as

$\sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}}$

Now, sicne both $4$ and $9$ are perfect squares

4 = 2 * 2 - 2""^2

9 = 3 * 3 = 3""^2

all you have to do is take the square root of both these numbers to get

$\frac{\sqrt{4}}{\sqrt{9}} = \sqrt{2 {\text{^2)/sqrt(3}}^{2}} = \textcolor{g r e e n}{\frac{2}{3}}$