Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 72

Answer

$\dfrac{2x^3y}{\sqrt[]{xyz}}$

Work Step by Step

Rationalizing the numerator of $ \sqrt[]{\dfrac{8x^5y}{2z}} $ results to \begin{array}{l} \sqrt[]{\dfrac{4x^4\cdot2xy}{2z}} \\\\= 2x^2\sqrt[]{\dfrac{2xy}{2z}} \\\\= 2x^2\sqrt[]{\dfrac{xy}{z}} \\\\= 2x^2\sqrt[]{\dfrac{xy}{z}} \cdot \sqrt[]{\dfrac{xy}{xy}} \\\\= 2x^2\sqrt[]{\dfrac{x^2y^2}{xyz}} \\\\= \dfrac{2x^2\cdot xy}{\sqrt[]{xyz}} \\\\= \dfrac{2x^3y}{\sqrt[]{xyz}} .\end{array}
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