Question

Find the cube root of 3375 by the method of prime factorization.
(a).15
(b).25
(c).35
(d).55

Answer 1

Hint: In this problem, we will follow the method of prime factorization to find the cube root of the given number by resolving them into its prime factors and then proceeding to the rules.

Complete step-by-step answer:

In order to find the cube root of a number by prime factorization method, we follow the given below step:

First of all, we reduce the given number into its prime factors.
We know that a prime number is a number which is only divisible by 1 and itself. Or, we can say that they have only two factors and they are 1 and the number itself.
After that we form a group of the factors. We group the factors in three in such a way that each number of the group is the same.
In the last step we take out a factor from each group and the final product of the factors is obtained. This product is the required value of the cube root of the number.
Since, the number given to us is 3375. On reducing 3375 into its prime factors, we get:
$3375=5\times 5\times 5\times 3\times 3\times 3$

After making group of three, we have:
$3375=\left( 5\times 5\times 5 \right)\times \left( 3\times 3\times 3 \right)$

After taking out one factor from each group and on multiplying them, we get:
Cube root of 3375 = $5\times 3=15$
So, the cube root of 3375 is 15.
Hence, option (a) is the correct answer.

Note: Students should note here that while doing prime factorization, it is not necessary that we start from the smallest prime factor that divides the given number. We can start dividing it by any number provided that the number is prime.