CLASS-8
FINDING CUBE ROOT BY PRIME FACTORIZATION METHOD

To Find the Cube Root by Prime Factorization 

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

Step.2) Make Triplets of equal prime factors.

Step.3) Take one Factor from each triplet and multiply them.

We can also express the number as a product of powers of prime factors, then dividing each index by 3 and multiplying the obtained factors we can find the cube root.

Example.1)  Find the cube root of 216000

So,  216000 = 10 X 10 X 10 X 3 X 3 X 3 X 2 X 2 X 2

=  (10 X 10 X 10) X (3 X 3 X 3) X (2 X 2 X 2)

=  10ᶟ X 3ᶟ X 2ᶟ

So,  ∛216000 = ∛(10ᶟ X 3ᶟ X 2ᶟ)

=  ∛10ᶟ X ∛3ᶟ X ∛2ᶟ

=  10 X 3 X 2 = 60

So, cube root of 216000 is 60    (Ans.)

Example.2)  Find the cube root of 42875

So, 42875 = 5 X 5 X 5 X 7 X 7 X 7

   =  (5 X 5 X 5) X (7 X 7 X 7)

   =  5ᶟ X 7ᶟ

So, ∛42875 = ∛(5ᶟ X 7ᶟ )

              =  ∛5ᶟ X ∛7ᶟ

              =  5 X 7 = 35 

So, the obtained cube root of 42875 is 35  (Ans.)