Answer
$2r^{4}s^{6}\sqrt (3r)$
Work Step by Step
$\sqrt (12r^{9}s^{12})=\sqrt (4\times r^{8} \times s^{12}\times 3r)=\sqrt 4\times \sqrt (r^{8})\times \sqrt (s^{12})\times \sqrt (3r)=2r^{4}s^{6}\sqrt (3r)$
We know that $\sqrt 4=2$, because $2^{2}=4$. We also know that $\sqrt (r^{8})=r^{4}$, because $(r^{4})^{2}=r^{4\times2}=r^{8}$ and that $\sqrt (s^{12})=s^{6}$, because $(s^{6})^{2}=s^{6\times2}=s^{12}$.
