# How do you find the square root of 36/49?

Jun 12, 2016

$\sqrt{\frac{36}{49}} = \textcolor{g r e e n}{\frac{6}{7}}$

#### Explanation:

In general
$\textcolor{w h i t e}{\text{XXX}} \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{36} = 6$

$\sqrt{49} = 7$

So
$\textcolor{w h i t e}{\text{XXX}} \sqrt{\frac{36}{49}} = \frac{\sqrt{36}}{\sqrt{49}} = \frac{6}{7}$

Jun 12, 2016

Answer is: $\pm \frac{6}{7}$, see explanation for steps.

#### Explanation:

Remember, or take a moment to learn, that:

$\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}$

To find the square root of a fraction, we can simply find the square root of the numerator and denominator:

$\frac{\sqrt{36}}{\sqrt{49}}$

Either by using a calculator or recalling information, we come to find that:

$\sqrt{36} = \pm 6$

and

$\sqrt{49} = \pm 7$

$\pm 6 / \pm 7$
$\pm \frac{6}{7}$
**The $\pm$ indicates that a number can be positive or negative, and in this case we use this symbol since the square root of a positive number always has a positive and negative answer. For example, if you multiply $6$ by itself, you get $36$. If you multiply $- 6$ by itself, you get $36$ as well. This is why we include the $\pm$ symbol, and it is the correct form of writing your answers.