#### Answer

$10y^{3}\sqrt y$

#### Work Step by Step

$\sqrt (10y^{7})=\sqrt (10\times y^{6}\times y)=\sqrt 10\times\sqrt y^{6}\times\sqrt y=10y^{3}\sqrt y$
We know that $\sqrt 100=10$, because $10^{2}=100$.
We know that $\sqrt y^{6}=y^{3}$, because $(y^{3})^{2}=y^{3\times2}=y^{6}$.