Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-1 Roots and Radical Expressions - Lesson Check: 9

Answer

The index $n$ is odd.

Work Step by Step

When the index of a radical is odd, then the given number has only one real nth root. On the other hand, when the index is a even, the given number has two real nth roots: one negative and one positive. Thus, if a number has only one real nth root, then the index $n$ is odd.
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