Elementary Algebra

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

Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 15


$ 5\sqrt[3] {3}/6$

Work Step by Step

When taking a cube root of a fraction, we take the cube root of the numerator (top of the fraction) and denominator (bottom of the fraction) separately. The cube root of 216 is 6, and there is no integer cube root of 375, giving us the expression of $\sqrt[3] {375}/6$ However, we know that 125, which is a perfect cube, is a factor of 375. Thus, we can simplify: $\sqrt[3] {125} \sqrt[3] {3} /6 = 5\sqrt[3] {3}/6$
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