jmc

Multiply both numerator and denominator by $\sqrt{3}$: $$\begin{array}{rl}\sqrt{\frac{2}{3}}& =\frac{\sqrt{2}}{\sqrt{3}}\\ & =\frac{\sqrt{2}}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}\\ & =\boxed{\frac{\sqrt{6}}{3}}.\end{array}$$