#### Answer

$2ab\sqrt{5b}$

#### Work Step by Step

$\sqrt{20a^2b^3}\longrightarrow$ factor out perfect square
=$\sqrt{4a^2b^2\times5b}\longrightarrow$ multiplication property of square roots
=$\sqrt{4a^2b^2}\times\sqrt{5b}\longrightarrow$ simplify
=$2ab\sqrt{5b}$