Question

find the smallest number by which 200 should be multiplied to make it a perfect cube​

Answer 1

Answer:

200=2×2×2×5×5

It should be multiplied by 5 to make it a perfect cube.

Answer 2

Given,

The main number is 200.

To find,

The smallest number that we need to multiply with the main number to get a perfect cube.

Solution,

First of all, we need to find out the prime factors of the given main number. And, we have to keep in mind that a perfect cube contains an individual prime factor in the number of three's multiple. So, for getting a perfect cube, we need to add factors for multiplication which are not in the number of three's multiples.

Prime factors of the main number :

200 = 2 × 2 × 2 × 5 × 5

Now, in the above mentioned prime factorization, there are two individual "5". So, to make it in the number of three's multiple, we need to add one "5" in the above multiplication sequence. The result of the new multiplication sequence, will be a perfect cube.

2×2×2×5×5×5 = 1000 = (10)³ [ A perfect cube]

Hence, the smallest number is 5.