Question

State the steps for finding the cube root of a given number by factorization ​

Answer 1

Answer:

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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