Intermediate Algebra (6th Edition)

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

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 52

Answer

$2y^{3}\sqrt[3] (5y)$

Work Step by Step

$\sqrt [3] (40y^{10})=\sqrt [3] (8y^{9}\times5y)=\sqrt [3] (8y^{9})\times \sqrt[3] (5y)=2y^{3}\sqrt[3] (5y)$ We know that $\sqrt[3] (8y^{9})=2y^{3}$, because $(2y^{3})^{3}=(2\times2\times2)\times y^{3\times3}=8y^{9}$.
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