Answer
$10a\sqrt {ab}$
Work Step by Step
$\sqrt {100a^{3}b}$
=$\sqrt {100}\times\sqrt {a^{3}}\times\sqrt {b}$
=$10\times \sqrt {a^{2}\times a}\times\sqrt {b}$
=$10\times a\sqrt {a}\times\sqrt {b}$
=$10\times a\times\sqrt {a}\times\sqrt {b}$
=$10a\times\sqrt {a\times b}$
=$10a\sqrt {ab}$