Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set - Page 718: 59



Work Step by Step

$\dfrac{\sqrt[3]{3x^{5}}}{10}$ First, simplify this expression: $\dfrac{\sqrt[3]{3x^{5}}}{10}=\dfrac{x\sqrt[3]{3x^{2}}}{10}=...$ Multiply this fraction by $\dfrac{\sqrt[3]{9x}}{\sqrt[3]{9x}}$ and simplify again if possible: $...=\dfrac{x\sqrt[3]{3x^{2}}}{10}\cdot\dfrac{\sqrt[3]{9x}}{\sqrt[3]{9x}}=\dfrac{x\sqrt[3]{27x^{3}}}{10\sqrt[3]{9x}}=\dfrac{x(3x)}{10\sqrt[3]{9x}}=\dfrac{3x^{2}}{10\sqrt[3]{9x}}$
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