Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set - Page 538: 24


$(3x - 2)\sqrt[3]{3x}$

Work Step by Step

Simplify each radical by factoring the radicand so that at least one factor is a perfect cube to obtain: $=\sqrt[3]{27x^3(3x)} - \sqrt[3]{8(3x)} \\=\sqrt[3]{(3x)^3(3x)} - \sqrt[3]{(2^3)(3x)} \\=3x\sqrt[3]{3x} - 2\sqrt[3]{3x}$ RECALL: The distributive property states that for any real numbers a, b, and c: (1) $ac + bc = (a+b)c$ (2) $ac-bc=(a-b)c$ Use the rule (2) above to combine like terms and obtain: $=(3x - 2)\sqrt[3]{3x}$
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