## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 7

#### Answer

$3\sqrt[3] {2}$

#### Work Step by Step

Recall, $\sqrt[3] a \times \sqrt[3] b = \sqrt[3] {a \times b}$. Thus, we can multiply 9 and 6 to obtain the simplified expression: $\sqrt[3] {9 \times 6} = \sqrt[3] {54}$ In order to simplify a cube root, we consider the factors of the number inside of the cube root. If any of these factors are perfect cubes, meaning that their cube root is an integer, then we can simplify the expression. We know that 27 and 2 are factors of 54. We know that 27 is a perfect cube, so we simplify: $\sqrt[3] {27} \sqrt[3] {2}=3\sqrt[3] {2}$

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