Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set: 73

Answer

$\dfrac{x^2y}{\sqrt[]{2xy}}$

Work Step by Step

Rationalizing the numerator, the given expression, $ \sqrt[]{\dfrac{x^3y}{2}} ,$ is equivalent to \begin{array}{l} \sqrt[]{\dfrac{x^3y}{2}\cdot\dfrac{xy}{xy}} \\\\= \sqrt[]{\dfrac{x^4y^2}{2xy}} \\\\= \sqrt[]{\dfrac{(x^2y)^2}{2xy}} \\\\= \dfrac{x^2y}{\sqrt[]{2xy}} .\end{array}
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