Finding cube root by prime factorisation method

Last updated at August 14, 2026 by

Let’s do this by examples

 

Find cube root of 216?

Let’s do prime factorization of 216

31.jpg

Thus,

  216  = 2 × 2 × 2 × 3 × 3 × 3

 

Now,

We make groups of 3

Finding cube root by prime factorisation method - Part 2

Therefore,

Cube root of 216 = 2 × 3

            = 6

 

Find cube root of 729?

Doing Prime factorization of 729

Finding cube root by prime factorisation method - Part 3

We see that

Finding cube root by prime factorisation method - Part 4

Therefore,

Cube root of 729 = 3 × 3

     = 9

 

Find cube root of 3375?

Doing Prime factorization of 3375

Finding cube root by prime factorisation method - Part 5

We see that

Finding cube root by prime factorisation method - Part 6

Therefore,

Cube root of 3375 = 3 × 5

       = 15

 

Find cube root of 6859?

Doing Prime factorization of 6859

Finding cube root by prime factorisation method - Part 7

We see that

Finding cube root by prime factorisation method - Part 8

Therefore,

Cube root of 6859 = 19

 

Find cube root of 10648?

Doing Prime factorization of 10648

Finding cube root by prime factorisation method - Part 9

We see that

Finding cube root by prime factorisation method - Part 10

Therefore,

Cube root of 10648 = 2 × 11

                = 22

 

Find cube root of 74088?

Doing Prime factorization of 74088

Finding cube root by prime factorisation method - Part 11

We see that

Finding cube root by prime factorisation method - Part 12

Therefore,

Cube root of 74088 = 2 × 3 × 7

                = 42

 

Remove Ads
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.