Answer
$3x^{2}y^{3}\sqrt (xy)$
Work Step by Step
$\sqrt (9x^{5}y^{7})=\sqrt (9\times x^{4}\times x \times y^{6}\times y)=\sqrt 9\times \sqrt (x^{4})\times \sqrt x \times \sqrt (y^{6})\times \sqrt y$
Further simplification:
$3x^{2}y^{3}(\sqrt x\times\sqrt y)=3x^{2}y^{3}\sqrt (xy)$
We know that $\sqrt 9=3$, because $3^{2}=9$.
We know that $\sqrt (x^{4})=x^{2}$, because $(x^{2})^{2}=x^{2\times2}=x^{4}$ and also that $\sqrt (y^{6})=y^{3}$, because $(y^{3})^{2}=y^{3\times2}=y^{6}$
