# Introduction to Cube root

In Math, there is always an "opposite" operation! The opposite operation for "cubing" a number is taking the "cube root".

Cube root is the opposite of cubing a number.

Term for raising a number to the 3rd power is "cubing a number".

For example:

23 = 8 this can be read as 2 "cubed" equals 8.

This means that 2 x 2 x 2 = 8.

We represent cube root using this symbol ‘ ’

And to show that cube root is opposite of cubing a number, let have a look at the following example:

23 = 8 and 8 = 2 x 2 x 2 = 2

Finding Cube Root by Prime Factorization

To find the cube root of a number by prime factorization, we follow the following steps:**Step I:** Find the prime factors of the given number.

**Make groups of 3 same factors.**

Step II:

Step II:

**Take one prime factor from each group of prime factors of the given number.**

Step III:

Step III:

**Find the product of these prime factors to get the cube root of the given number.**

Step IV:

Step IV:

Let’s understand this with example:

Find the cube root of 3375 by prime factorization.

**Step I:**Find the prime factors of the given number.

3375 = 3 x 3 x 3 x 5 x 5 x 5

**Step II:**Make groups of 3 same factors.

(3 x 3 x 3)

(5 x 5 x 5)

**Step III:**Take one prime factor from each group of prime factors of the given number.

(3 x 3 x 3) – 3

(5 x 5 x 5) – 5

**Step IV:**Find the product of these prime factors to get the cube root of the given number.

3 x 5 = 15

Hence the cube root of 3375 is 15.

Let’s try more examples to understand the concept better:

Find cube root of 5832 by prime factorization.

**Step I:** Find the prime factors of 5832

5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3**Step II:** Make groups of three same factors

2 x 2 x 2

3 x 3 x 3

3 x 3 x 3**Step III:** Take one prime factor from each group of prime factors of 5832

2 x 2 x 2 - 2

3 x 3 x 3 - 3

3 x 3 x 3 – 3**Step IV:** Find the product of these prime factors to get the cube root of the given number.

2 x 3 x 3 = 18

So, Cube root of 5832 is 18.

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