Answer
$5ab\sqrt b$
Work Step by Step
$\sqrt (25a^{2}b^{3})=\sqrt (25\times a^{2}\times b^{2}\times b)=\sqrt 25\times \sqrt (a^{2})\times \sqrt (b^{2})\times\sqrt b=5ab\sqrt b$
We know that $\sqrt 25=5$, because $5^{2}=25$.
We know that $\sqrt (a^{2})=a$, because $(a)^{2}=a^{2}$, and also that $\sqrt (b^{2})=b$, because $(b)^{2}=b^{2}$.
