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In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 and can be written as 3 × 3.
The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n, usually pronounced as "n squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square. Hence, a square with side length n has area n. If a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers.
Square numbers are non-negative. A non-negative integer is a square number when its square root is again an integer. For example, 9 = 3 , {\displaystyle {\sqrt {9}}=3,} so 9 is a square number.
A positive integer that has no square divisors except 1 is called square-free.