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.

One way of doing this is to use prime factorization.

2352 = 3 x 4 x 4 x 7 x 7

Looking at the above numbers, we see that if there was another 3 factor, it would be a perfect square.

So if our number was 3 x 3 x 4 x 4 x 7 x 7, it would be a perfect square.

That number multiplies out to be 7056.  The square root of this number would be 3 x 4 x 7 = 84.  Yay!