Question

What is the cube root in factorzation method

Answer 1

In order of finding cube root by prime factorization we use the following steps :

Step I : Obtain the given number.
Step II : Resolve it into prime factors.
Step III : Group the factors in 3 in such a way that each number of the group is same.
Step IV : Take one factor from each group.
Step V : Find the product of the factors obtained in step IV. This product is the required cube root.

Examples : Finding the cube root by prime factorization

1) ∛64
Solution :
64 = 2 x 32
= 2 x 2 x 16
= 2 x 2 x 2 x 8
= 2 x 2 x 2 x 2 x 4
= 2 x 2 x 2 x 2 x 2 x 2 (make the groups of 3 of equal numbers)
There are two groups, so from each group take one factor
∴ ∛64 = 2 x 2
∴ ∛64 = 4