The first six square numbers are 1, 4, 9, 16, 25 and 36. A square number, or a perfect square, is an integer that is the square of an integer. In other words, it is the product of some integer with itself.
The usual notation for the formula for the square of a number n is not the product of n?×?n, but the equivalent exponentiation n to the power of 2, usually pronounced as "n squared." The name "square number" comes from the name of the shape.
Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number is that its square roots are integers. A positive integer that has no perfect square divisors except 1 is called square-free.
The unit of area is defined as the area of unit square (1?×?1). A square number is also the sum of two consecutive triangular numbers. The sum of two consecutive square numbers is a centered square number. Every odd square is also a centered octagonal number. A square number also has an odd number of positive divisors, while other natural numbers have an even number of positive divisors. An integer root is the only divisor that pairs up with itself to yield the square number, while other divisors come in pairs.