Square number

Square numbers are numbers of the form $$n^2$$ and is equal to n × n.

They are: 1, 4, 9, 16, 25, 36, 49, 64, ...

All square numbers except 1 are composite numbers and they are positive integers.

A square number is even if its square root is even, and a square number is odd if its square root is odd.

As the square root of a negative number is an imaginary number, which is not an integer, there are only positive numbers which are square numbers.

Subtracted by 1
See also: n^2 - 1 (sequence)

These numbers are of the form (n - 1)(n + 1), and all are composite except 0 and 3.

Square triangular numbers
A square triangular number is a number that is both a triangular number and a square number. The first number to be a square triangular number is 36, the 6th square number and the 8th triangular number.

Ending with 5
Square numbers ending with 5 actually end with 25. They are easier to find than normal square numbers and are of the form $$(10n + 5)^2 = 100n(n + 1) + 25$$. There is an algebraic proof that this works for all integers n.

Ending with 0
Square numbers ending with 0 actually end with 00. They can be found by finding the square of one tenth of the number which will be squared and add '00' to the end of it. This happens as 102 = 100.