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: 28



Work Step by Step

Factor the radicand of the first radical so that one factor is a perfect cube. Then, simplify to obtain: $=4\sqrt[3]{x^3(xy^2)}+5x\sqrt[3]{xy^2} \\=4(x)\sqrt[3]{xy^2} + 5x\sqrt[3]{xy^2} \\=4x\sqrt[3]{xy^2} + 5x\sqrt[3]{xy^2}$ 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 (1) above to combine like terms and obtain: $=(4x+5x)\sqrt[3]{xy^2} \\=9x\sqrt[3]{xy^2}$
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