Finding Cube Root by Prime Factorization

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

Cube of Numbers
Perfect Cube
Properties of Cube
Cube by Column method
Cube of Negative numbers
Cube of Rational numbers
Cube Root
Finding cube root by Prime Factorization
Cube root of Rational numbers
Estimating cube root

From Cube root to Exponents

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