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3 votes
3 votes
Find the indicated real nth root(s) of a.
n=3, a = - 216

User Matszwecja
by
2.4k points

1 Answer

28 votes
28 votes

Answer:

-6

Explanation:

A suitable calculator can find this for you directly.

Odd root of a negative number

-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:

∛(-216) = -∛216 = -6

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Additional comment

Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.

The second attachment shows a calculator capable of finding the complex roots as well as the real one.

Find the indicated real nth root(s) of a. n=3, a = - 216-example-1
Find the indicated real nth root(s) of a. n=3, a = - 216-example-2
User Christopher Bonitz
by
2.9k points