## Elementary Algebra

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