## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 25

#### 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: $\sqrt {12a^{2}b^{3}}$ =$\sqrt {12}\times\sqrt {a^{2}}\times\sqrt {b^{3}}$ =$\sqrt {4\times3}\times\sqrt {a^{2}}\times\sqrt {b^{2}\times b}$ =$\sqrt {2^{2}\times3}\times\sqrt {a^{2}}\times\sqrt {b^{2}\times b}$ =$2\sqrt {3}\times a\times b\sqrt {b}$ =$2\times a\times b\times\sqrt {3}\times \sqrt {b}$ =$2ab\times\sqrt {3\times b}$ =$2ab\sqrt {3b}$

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