Square Number

This formula says that the nth square number is found by multiplying n by itself, so the sequence goes 1, 4, 9, 16, 25, and so on. It works because a square number represents the area of a square with side length n: if each side has n unit lengths, the total number of unit squares inside is n × n = n^2. In other words, every perfect square comes from pairing equal factors.

Use this when you need the value of a perfect square, such as in counting grids, geometry, or identifying square numbers in sequences. It also helps when checking whether a number can be written as an integer times itself.

• Using n + 2 instead of n^2
• Forgetting that the index n is squared, not doubled
• Assuming every large number is a square just because it is even