# How do you rationalize the denominator and simplify (6 sqrt 5)/(5 sqrt 3)?

To get rid of radicals under the division bar, multiply both top and bottom by the same root $\sqrt{3}$:
$\frac{6 \sqrt{5}}{5 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{6 \sqrt{5} \cdot \sqrt{3}}{5 {\sqrt{3}}^{2}} = \frac{6 \sqrt{15}}{5 \cdot 3} = \frac{2}{5} \sqrt{15}$