Question

Smallest number to be multiplied with 2880 to make a perfect square is

Answer 1

Answer:

The smallest number to be multiplied with 2880 to make a perfect square is 5.

Answer 2

Given: A number 2880

To find: The smallest number to be multiplied with 2880 to make it a perfect square

Solution: Using Prime factorization, we get

2880 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5

We can see that prime factorization of 2880 consists three pairs of 2 and one pair of 3, while 5 couldn't make any pair.

It is clear that in order to get a perfect square, one more 5 is required.

i.e., 2880 × 5 = 14400 (which is a perfect square).

Hence, the smallest number to be multiplied with 2880 to make it a perfect square is 5.