# How do you simplify: square root of 300 divided by the square root of 6?

Jul 23, 2015

square root of 300 divided by the square root of 6 $= \pm 5 \sqrt{2}$

#### Explanation:

(Assuming your use of the phrase "square root" is intended to include both positive and negative roots... as opposed to the symbol $\sqrt{\text{something}}$ which is defined to be only the positive roots):

Since $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$\pm \frac{\sqrt{300}}{\sqrt{6}} = \pm \sqrt{50}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \pm \sqrt{{5}^{2} \cdot 2}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \pm \sqrt{{5}^{2}} \cdot \sqrt{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \pm 5 \sqrt{2}$