Finding cube root by prime factorisation method

Last updated at April 16, 2024 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

 

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.