College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 66

Answer

$\sqrt[4]{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt[4]{\sqrt{25}} ,$ use the definition of rational exponents. $\bf{\text{Solution Details:}}$ Since $\sqrt{25}=5,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{5} .\end{array} Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 5^{\frac{1}{4}} \\\\= 5^{1/4} \\\\= \sqrt[4]{5} .\end{array}
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.