A cube root is also known as the third root. When solving for the cube root of term, you are looking for what value, multiplied by itself 3 times, would give you the base.

Example:
8 = 2, because 2 x 2 x 2 = 8.

The number under the radical, 8, is known as the base. The root is 3 for all cube roots.

Example:
64 = 4, because 4 x 4 x 4 = 64. The base is 64, and the root is 3.

We can also have negative numbers under a cube root. Using our knowledge of multiplication with negative numbers, we can deduce that this can occur if a negative number is multiplied with itself 3 times. So, if our base is negative, our answer must also be negative.

Example:
-27 = -3, because -3 x -3 x -3 = -27

Take care! Taking a cube root is very different than dividing by three. For instance, a common error for the previous problem is :

-27 = -9, because -9 x 3 = -27

Make sure you do not commit this error, as multiplication by 3 and multiplication by oneself three times are very different.

Practice Problems

Simplify

1. 125

2. 729

3. -8

4. Mandy simplified a cube root problem and was told she got the wrong answer. Can you tell her where she went wrong? What is the correct answer:

-216 = -72, because -72 x 3 = -216

Answers

1. 125 = 5, because 5 x 5 x 5 = 125.

2. 729 = 9, because 9 x 9 x 9 = 729

3. -8 = -2, because -2 x -2 x -2 = -8. Notice that, since our base was negative, our answer had to be negative.

4. Mandy divided by 3 when she was supposed to find the cube root, or the number that, when multiplied with itself 3 times, gave her the base.

-216 = -6, because -6 x -6 x -6 = -216.

Note that our answer is negative because our base was negative.

Related Links: Math algebra Dividing with Square Roots Introduction to Cube Roots Multiplying Square Roots with Exponents Multiplying Square Roots