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: 21



Work Step by Step

Simplify each radical by factoring the radicand so that at least one factor is a perfect cube to obtain: $=\sqrt[3]{27y^3(2x)} + y\sqrt[3]{64(2x)} \\=\sqrt[3]{(3y)^3(2x)} + y\sqrt[3]{(4^3)(2x)} \\=3y\sqrt[3]{2x} + 4y\sqrt[3]{2x}$ 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 rule (1) above to combine like terms and obtain: $=(3y+4y)\sqrt[3]{2x} \\=7y\sqrt[3]{2x}$
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