Properties of square numbers:

• The ending digit of a square number can only be $0$, $1$, $4$, $5$, $6$, and $9$.
• If $n$ is even, then $n^2$ must be multiple of $4$.
• If $n$ is odd, then the remainder when $n^2$ is divided by $4$ or $8$ must be one.
• The sum of two squares cannot be in the form of $4K+3$. In another word, the remainder when the sum is divided by $4$ cannot be $3$.
• A square number will have an odd number of divisors. On the other hand, if an integer has an odd number of divisors, then it must be a square number.

Please refer to the video or the attached PDF for more fun facts of square numbers.