What are square number?

Square numbers are the products of numbers that have been multiplied by themselves like 2 x 2 = 4, or 9 X 9 = 81. The squares here are 4 and 81.

Numbers that can be made by multiplying another number my itself, like 12 x 12 = 144. So 144 is a square number.

By convention and probably also by definition, square numbers and square roots (the numbers multiplied by themselves) are always whole numbers, integers with no factional or decimal parts.
A square number is the result of any non-zero integer multiplied by itself.

9 is a square number because 3 x 3 = 9.

5 is not a square number because there isn't an integer that can be multiplied by itself to make 5.