Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 551: 108



Work Step by Step

Rationalize $\displaystyle \frac{20}{ \sqrt[3]{2}}$ $\displaystyle \frac{20}{ \sqrt[3]{2}}\color{red}{ \cdot\frac{ \sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}} }=\frac{20\sqrt[3]{2^{2}}}{\sqrt[3]{2^{3}}}=\frac{20\sqrt[3]{4}}{2}=10\sqrt[3]{4}$ $\displaystyle \sqrt[4]{8}-\frac{20}{ \sqrt[3]{2}}=\sqrt[4]{8}-10\sqrt[3]{4}$ $\sqrt[4]{8}=\sqrt[4\cdot 3]{8^{3}}=\sqrt[12]{512}$ $\sqrt[3]{4}=\sqrt[3\cdot 4]{4^{4}}=\sqrt[12]{256}\quad$ so there are no common terms and we can not simplify further.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.