Which one of the following numbers is not a square of any integer?

A number is a perfect square if all of its prime factors have even exponents. As the question deals with such large numbers it's probably best to skip prime factorising each and every answer choice and to see if there isn't a pattern within smaller perfect squares that one can work with.

Looking at the first few perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169... one can see that the units digits are a set of numbers which repeat: 1, 4, 6, 9 and 00. This shows that no perfect square will end in 2, 3, 7 or 8.

Looking at our answer choices D ends in 2. Thus, this will most likely be the answer.

To double check
63952/2 = 31796
31796/2 = 15898
15898/2 = 7949

As 7949 is odd, and all other prime numbers besides 2 are odd, it is impossible that there will be another even number to divide by 2 during prime factorisation as odd/odd = odd. Thus 2 will have an exponent of 3 which means that 63952 does not have a perfect square.

Answer D.