# Finding Cube Root by Prime Factorization

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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
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2)
 ∛13824 Solution : After resolving the prime factors, we get 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 Grouping = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 Taking one factor from each group ∛13824 = 2 x 2 x 2 x 3 ∛13824 = 24 Cube and Cube Roots

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