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: 20

Answer

$(24x+1)\sqrt{5x}$

Work Step by Step

Simplify the first radical by factoring the radicand so that at least one factor is a perfect square to obtain: $=8\sqrt{9x^2(5x)} + \sqrt{5x} \\=8\sqrt{(3x)^2(5x)} + \sqrt{5x} \\=8(3x)\sqrt{5x} + \sqrt{5x} \\=24x\sqrt{5x} + \sqrt{5x}$ 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: $=(24x+1)\sqrt{5x}$
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