# How do you rationalize sqrt22/sqrt33?

$\frac{\sqrt{22}}{\sqrt{33}} = \sqrt{\frac{22}{33}} =$ divide both by $11$ $= \sqrt{\frac{2}{3}}$
$\sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} = \frac{\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{6}}{3}$
$\frac{\sqrt{22}}{\sqrt{33}} \cdot \frac{\sqrt{33}}{\sqrt{33}} = \frac{\sqrt{22 \cdot 33}}{33} = \frac{\sqrt{\left(2 \cdot 11\right) \left(3 \cdot 11\right)}}{33} = \frac{\sqrt{6 \cdot {11}^{2}}}{33} = \frac{11}{33} \sqrt{6} = \frac{\sqrt{6}}{3}$