Question

find all the cube roots of -216.
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the real cube root(s) of -216 is/are .
(simplify your answer. use a comma to separate answers as needed.)
b. there are no real cube roots of -216.

Explanation:

Step1: Recall the definition of cube root

A cube root of a number \( x \) is a number \( y \) such that \( y^3=x \). We need to find \( y \) such that \( y^3 = - 216\).

Step2: Find the number whose cube is -216

We know that \( (-6)\times(-6)\times(-6)=(-6)^3=-216 \). Also, for real numbers, the cube root of a negative number is negative. And every real number has exactly one real cube root.

Answer:

A. The real cube root(s) of -216 is/are \(-6\).