# How do you simplify sqrt18/sqrt3?

Jun 6, 2015

Knowing that $\frac{\sqrt{A}}{\sqrt{B}} = \sqrt{\frac{A}{B}}$ then

$\frac{\sqrt{18}}{\sqrt{3}} = \sqrt{\frac{18}{3}} = \sqrt{6}$

Jun 6, 2015

You can take a one big square root:
$\sqrt{\frac{18}{3}} = \sqrt{6}$
Or:
Multiply and divide by $\sqrt{3}$:
$\frac{\sqrt{18}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{6 \cdot 3} \cdot \sqrt{3}}{3} = \frac{\sqrt{6} \sqrt{3} \sqrt{3}}{3} =$
$= \cancel{3} \frac{\sqrt{6}}{\cancel{3}} = \sqrt{6}$