Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 710: 42



Work Step by Step

$\dfrac{\sqrt[3]{3}}{10}+\sqrt[3]{\dfrac{24}{125}}$ Rewrite the second term as $\dfrac{\sqrt[3]{8\cdot3}}{\sqrt[3]{125}}$ and simplify it: $\dfrac{\sqrt[3]{3}}{10}+\sqrt[3]{\dfrac{24}{125}}=\dfrac{\sqrt[3]{3}}{10}+\dfrac{\sqrt[3]{8\cdot3}}{\sqrt[3]{125}}=\dfrac{\sqrt[3]{3}}{10}+\dfrac{2\sqrt[3]{3}}{5}=...$ Evaluate the sum and simplify if possible: $...=\Big(\dfrac{1+2\cdot2}{10}\Big)\sqrt[3]{3}=\dfrac{5}{10}\sqrt[3]{3}=\dfrac{\sqrt[3]{3}}{2}$
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