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 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set: 41

Answer

$x^4y^4\sqrt{y}$

Work Step by Step

Factor the radicand (expression inside the radical sign) so that at least one factor is a square to obtain: $=\sqrt{x^8y^8(y)} \\=\sqrt{(x^4y^4)^2(y)}$ The principal square root is always non-negative. However, the value of $x^4y^4$ will never be negative, so we do not need to add absolute value bars. Thus, $\sqrt{(x^4y^4)^2(y)}=x^4y^4\sqrt{y}$
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