# How do you simplify sqrt(14x) div sqrt(18x)?

Mar 28, 2018

$\frac{\sqrt{7}}{3}$

#### Explanation:

The key realization here is that we can separate the constants from the $x$s. Doing this, we have:

$\frac{\sqrt{14 x}}{\sqrt{18 x}} = \left(\frac{\sqrt{14}}{\sqrt{18}}\right) \cdot \left(\cancel{\frac{\sqrt{x}}{\sqrt{x}}}\right)$

$\implies \frac{\sqrt{14}}{\sqrt{18}}$

We can break up the radicals into the following:

$\frac{\sqrt{14}}{\sqrt{18}} = \frac{\sqrt{2 \cdot 7}}{\sqrt{2 \cdot 9}} = \frac{\cancel{\sqrt{2}} \cdot \sqrt{7}}{\cancel{\sqrt{2}} \cdot \sqrt{9}}$

$\sqrt{2}$ cancels with itself, and we get

$= \frac{\sqrt{7}}{\sqrt{9}}$

Which can be simplified to:

$\frac{\sqrt{7}}{3}$

Hope this helps!