#### Answer

$2ab\sqrt {3b}$

#### Work Step by Step

We break the square roots into their factors, and then we simplify the factors that are perfect squares:
$\sqrt {12a^{2}b^{3}}$
=$\sqrt {12}\times\sqrt {a^{2}}\times\sqrt {b^{3}}$
=$\sqrt {4\times3}\times\sqrt {a^{2}}\times\sqrt {b^{2}\times b}$
=$\sqrt {2^{2}\times3}\times\sqrt {a^{2}}\times\sqrt {b^{2}\times b}$
=$2\sqrt {3}\times a\times b\sqrt {b}$
=$2\times a\times b\times\sqrt {3}\times \sqrt {b}$
=$2ab\times\sqrt {3\times b}$
=$2ab\sqrt {3b}$