Before learning how to find the cube root, let us first learn the meaning of cube. The process of cubing a number is multiplying the number three times. The exponent used for cubes is 3, which is also denoted by the x^{3}. For example: The cube of 4 will be calculated as 4 * 4 * 4 = 4³ = 64 or 8³ = 8 * 8 * 8 = 512.

Now in order to find the cube root of a number the only method available is prime factorization. The approach applied is that each of the number, which is a perfect cube, will have every prime factor appearing in a group of 3. This is done because unlike square root there is no other conventional method to find the cube root. After the prime factorization, each of the prime factors is selected once for every three times it is appearing in the number. You will understand the concept better with the help of the following examples.

Prime factorization of 1728 is = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3

= (2 * 2 * 3) * (2 * 2 * 3) * (2 * 2 * 3).

= 12 * 12 * 12 the cube root of 1728 is 12.

= (2 * 2 * 3) * (2 * 2 * 3) * (2 * 2 * 3).

= 12 * 12 * 12 the cube root of 1728 is 12.

= (7 * 3) * (7 * 3) * (7 × 3)

= 21 * 21 * 21 Þ the cube root of 9261 is 21.

= 21 * 21 * 21 Þ the cube root of 9261 is 21.

= (5 * 5) * (5 * 5) * (5 * 5)

=25 * 25 * 25 Þ the cube root of 15625 is 25.

=25 * 25 * 25 Þ the cube root of 15625 is 25.

Now the prime factorization of 27 is 3 * 3 * 3. As you know, you need to take one number for every group of three. As 3 appear three times, taking a single 3 for the same, the cube root of 27 is 3.