Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.1 - Radical Expressions and Graphs - 7.1 Exercises - Page 440: 30


not a real number

Work Step by Step

We know that $\sqrt[8] -1$ is not a real number, because there is no number $a$ such that $a^{8}=-1$. In general, the nth root of a, written as $\sqrt[n] a$, will not be a real number if $a$ (also known as the radicand) is negative and $n$ (also known as the index) is positive.
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