## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 9

#### Answer

$4 \sqrt{6}$

#### Work Step by Step

Recall, $\sqrt{a}\times \sqrt{b}= \sqrt{a \times b}$. Thus, we can multiply 8 and 12 to obtain the simplified expression: $\sqrt{8 \times 12}=\sqrt{96}$ In order to simplify a radical, we consider the factors of the number inside of the radical. If any of these factors are perfect squares, meaning that their square root is a whole number, then we can simplify the radical. We know that 6 and 16 are factors of 96. We know that 16 is a perfect square, so we simplify: $\sqrt{16} \sqrt{6}=4 \sqrt{6}$

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