Questions: Find the cube root. ∛(-216) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The cube root is □ B. The cube root is not a real number.

Find the cube root.
∛(-216)

Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The cube root is □
B. The cube root is not a real number.

Transcript text: Find the cube root. \[ \sqrt[3]{-216} \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The cube root is $\square$ B. The cube root is not a real number.

Solution

Solution Steps

To find the cube root of $-216$, we need to determine the number which, when multiplied by itself three times, equals $-216$. Since the cube root of a negative number is also negative, we can find the cube root of the positive counterpart and then apply the negative sign.

Step 1: Identify the Cube Root of a Negative Number

To find the cube root of $-216$, we need to determine the number which, when multiplied by itself three times, equals $-216$. The cube root of a negative number is also negative.

Step 2: Calculate the Cube Root

The cube root of $-216$ can be calculated as: \[ \sqrt[3]{-216} = -\sqrt[3]{216} \]

Step 3: Simplify the Cube Root of the Positive Counterpart

The cube root of $216$ is: \[ \sqrt[3]{216} = 6 \]

Step 4: Apply the Negative Sign

Thus, the cube root of $-216$ is: \[ \sqrt[3]{-216} = -6 \]