Question

Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number.

Answer 1

We have 2352 = 2 × 2 × 2 × 2 × 3 × 7 × 7

As the prime factor 3 has no pair, 2352 is not a perfect square.

If 3 gets a pair then the number will become perfect square. So, we multiply 2352 by 3 to get,

2352 × 3 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7

Now each prime factor is in a pair.

Therefore, 2352 × 3 = 7056 is a perfect square.

Thus the required smallest multiple of 2352 is 7056 which is a perfect square.

And, `sqrt(7056)` = 2 × 2 × 3 × 7 = 84.