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: 6

Answer

$\dfrac{6}{\sqrt[3]{9}}=2\sqrt[3]{3}$

Work Step by Step

$\dfrac{6}{\sqrt[3]{9}}$ Multiply the whole equation by $\dfrac{\sqrt[3]{9^{2}}}{\sqrt[3]{9^{2}}}$: $\dfrac{6}{\sqrt[3]{9}}=\dfrac{6}{\sqrt[3]{9}}\cdot\dfrac{\sqrt[3]{9^{2}}}{\sqrt[3]{9^{2}}}=\dfrac{6\sqrt[3]{81}}{\sqrt[3]{9^{3}}}=\dfrac{6\sqrt[3]{81}}{9}=...$ Rewrite the expression as $\dfrac{6\sqrt[3]{27\cdot3}}{9}$ and simplify: $...=\dfrac{6\sqrt[3]{27\cdot3}}{9}=\dfrac{6(3)\sqrt[3]{3}}{9}=\dfrac{18\sqrt[3]{3}}{9}=2\sqrt[3]{3}$
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