Question

Find the cube root numbers by prime factorisation method: - 54872

Answer 1

Hint: Here in this method we will find prime factors of the given number and then will group together the same numbers to get the cube root of the given number.
Prime factorization is used to break down the number as a product of prime numbers, so when prime numbers come more than one time then they can be shown as in exponential form to make it compact.

Complete step-by-step answer:
So in this question we will find prime factors. To start with we will divide the number by 2 which is the smallest prime number and the factor which will come is again divided by 2 we keep on dividing the number by 2 until its number becomes not divisible by 3 and then we will try to divide the number by 3 and so on.
2 and 19 are prime factors of 54873.
Therefore prime factors of 54872 are:-
$ \Rightarrow 54872 = 2 \times 2 \times 2 \times 19 \times 19 \times 19$
$ \Rightarrow 54872 = (2 \times 19) \times (2 \times 19) \times (2 \times 19)$
$ \Rightarrow 54872 = (38) \times (38) \times (38)$
Now we will arrange 38 in exponential form
$ \Rightarrow 54872 = {(38)^3}$
$ \Rightarrow \sqrt[3]{{54872}} = 38$

Therefore we can say that the cube root of 54872 is 38.

Note: Students may find difficulty in determining if the number is divisible or not divisible by 2 so below mentioned divisibility test of 2 and 3.
Divisibility test of 2= If unit place of a number contains 2,4,6,8,0 then that number is divisible by 2
Divisibility test of 3= If sum of digits of a number comes as a factor of 3 then it will divisible by 3