Answer
$3x^{3}y^{4}\sqrt (xy)$
Work Step by Step
$\sqrt (9x^{7}y^{9})=\sqrt (9\times x^{6} \times y^{8}\times xy)=\sqrt 9\times \sqrt (x^{6})\times \sqrt (y^{8})\times \sqrt (xy)=3x^{3}y^{4}\sqrt (xy)$
We know that $\sqrt 9=3$, because $3^{2}=9$. We also know that $\sqrt (x^{6})=x^{3}$, because $(x^{3})^{2}=x^{3\times2}=x^{6}$ and that $\sqrt (y^{8})=y^{4}$, because $(y^{4})^{2}=y^{4\times2}=y^{8}$.
