Question

find all the cube roots of -512.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the real cube root(s) of -512 is/are .
(simplify your answer. use a comma to separate answers as needed.)

b. there are no real cube roots of -512.

Explanation:

Step1: Recall cube root definition

We need $x$ such that $x^3 = -512$.

Step2: Find real cube root

Calculate $(-8)^3 = (-8)\times(-8)\times(-8) = 64\times(-8) = -512$.

Answer:

A. The real cube root(s) of -512 is/are -8.