The numbers up to 100 that are perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. A perfect square is a number that is the result of a smaller number multiplied by itself.
Square numbers follow the form n^2, where "n" is a whole number. This is the same as n x n. With a given number that is a perfect square, you can find the next number that is a perfect square. For example, if you are given the number 16, which has a root of four, you can add four and five to get nine and add this to 16. This equals 25, which is a perfect square of root five. One important point is that a perfect square can not be negative. Taking the root of a negative number would lead to an imaginary number.
The history of square roots dates back to the ancient Egyptians. While the exact methodology of how these individuals arrived at finding these numbers isn't known, one conjecture is that they used a right angle with two equal arms. The two arms were multiplied and a perfect square was produced. A second right angle would produce a square.