CLASS-7
CUBE ROOT BY PRIME FACTORIZATION METHOD

To Finding Cube Root by Prime Factorization 

1) Express the number as a product of prime factors.

2) Make Triplets of equal prime factors.

3) Make one factor from each triplet and multiply them

We can also express number as a product of powers of prime factors. Then dividing each index by 3 and multiplying the factors will give us the cube root.

Example-

1) Find the cube root of 27000

     27000 = 10 X 10 X 10 X 3 X 3 X 3

³√27000  =  ³√10 X 10 X 10 X 3 X 3 X 3               

            =   10 X 3 =  30

2) Find the cube root of 3375

       3375  = 10 X 10 X 10 X 3 X 3 X 3

   ³√3375  =  ³√5 X 5 X 5 X 3 X 3 X 3             

             =    ³√5ᶟ  X   ³√3ᶟ

             =   5 X 3 =  15