# What is the square root of 14 divided by the square root of 45?

Oct 18, 2015

(Nothing really pretty)
$\frac{\sqrt{14}}{\sqrt{45}} = \frac{\sqrt{21}}{9}$

#### Explanation:

$\frac{\sqrt{14}}{\sqrt{45}}$

Factoring:
$\textcolor{w h i t e}{\text{XXXX}} = \frac{\cancel{\sqrt{2}} \cdot \sqrt{7}}{\sqrt{3} \cdot \sqrt{3} \cdot \sqrt{3} \cdot \cancel{\sqrt{2}}}$

Simplifying:
$\textcolor{w h i t e}{\text{XXXX}} = \frac{\sqrt{7}}{3 \sqrt{3}}$

Rationalizing the denominator (by multiplying both numerator and denominator by $\left(\sqrt{3}\right)$
$\textcolor{w h i t e}{\text{XXXX}} = \frac{\sqrt{21}}{9}$