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: 17

Answer

$13\sqrt[3]{2}$

Work Step by Step

Simplify each radical to obtain: $=5\sqrt[3]{8(2)} + \sqrt[3]{27(2)} \\=5\sqrt[3]{2^3(2)} + \sqrt[3]{3^3(2)} \\=5(2)\sqrt[3]{2} + 3\sqrt[3]{2} \\=10\sqrt[3]{2} + 3\sqrt[3]{2}$ 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 rule (1) above to combine like terms and obtain: $=(10+3)\sqrt[3]{2} \\=13\sqrt[3]{2}$
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