1. The problem is to understand perfect and non-perfect squares. 2. A perfect square is a number that can be expressed as $n^2$ where $n$ is an integer. For example, $1, 4, 9, 16, 25$ are perfect squares because they are $1^2, 2^2, 3^2, 4^2, 5^2$ respectively. 3. Non-perfect squares are numbers that cannot be expressed as the square of an integer. For example, $2, 3, 5, 6$ are non-perfect squares. 4. To check if a number is a perfect square, find its square root and see if the result is an integer. 5. For example, to check if $36$ is a perfect square, calculate $\sqrt{36} = 6$, which is an integer, so $36$ is a perfect square. 6. To check if $20$ is a perfect square, calculate $\sqrt{20} \approx 4.47$, which is not an integer, so $20$ is not a perfect square. 7. Remember, perfect squares have whole number square roots, non-perfect squares do not.