Finding cube root by prime factorisation method

Let’s do this by examples

Find cube root of 216?

Let’s do prime factorization of 216

Thus,

  216  = 2 × 2 × 2 × 3 × 3 × 3

Now,

We make groups of 3

Therefore,

Cube root of 216 = 2 × 3

            = 6

Find cube root of 729?

Doing Prime factorization of 729

We see that

Therefore,

Cube root of 729 = 3 × 3

     = 9

Find cube root of 3375?

Doing Prime factorization of 3375

We see that

Therefore,

Cube root of 3375 = 3 × 5

       = 15

Find cube root of 6859?

Doing Prime factorization of 6859

We see that

Therefore,

Cube root of 6859 = 19

Find cube root of 10648?

Doing Prime factorization of 10648

We see that

Therefore,

Cube root of 10648 = 2 × 11

                = 22

Find cube root of 74088?

Doing Prime factorization of 74088

We see that

Therefore,

Cube root of 74088 = 2 × 3 × 7

                = 42