How Do You Simplify Cube Roots?

Simplify a cube root expression by factoring out the cube of a whole number if one is present. Continue factoring until the expression no longer contains the cube of a whole number, and solve for any cube roots of whole numbers that are present.

1. Find the factors of the cube root

Find the factors of the number under the radical sign. The factors are numbers that when multiplied together equal the number. For example, the number 54 can also be expressed as 9 x 2. Continue factoring until all the factors are prime numbers. For 54, the final prime factorization is 3 x 3 x 3 x 2.

2. Factor out numbers appearing three times

To simplify the cube root, factor out any prime factor that appears three times into its own cubic root expression. For example, the cube root of 54, which factors into the cube root 3 x 3 x 3 x 2, is factored as the cube root of 3 x 3 x 3 times the cube root of 2.

3. Solve for the cube root of a whole number

Since the cube of a number is that number multiplied by itself twice, the cube root of an expression x * x * x is equal to x. For example, the cube root of 3 x 3 x 3 is equal to 3. After the cubes of all whole numbers are removed from the expression, the cube root is in simplified form.