Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 13


$-10\sqrt[3] {3}$

Work Step by Step

First of all, in order to make this one large cube root, we multiply the coefficients to obtain that the new coefficient is -5. Recall, $\sqrt[3] a \times \sqrt[3] b = \sqrt[3] {a \times b}$. Thus, we can multiply 6 and 4 to obtain the simplified expression: $-5\sqrt[3] {6 \times 4} =-5 \sqrt[3] {24}$ 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 8 and 3 are factors of 24. We know that 8 is a perfect cube, so we simplify: $-5\sqrt[3] {8} \sqrt[3] {3}=-10\sqrt[3] {3}$
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