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| - In mathematics, a square number, sometimes also called 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. So, for example, 9 is a square number, since it can be written as 3 × 3. The usual notation for the formula for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name square number comes from the name of the shape. This is because a square with side length has area .
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abstract
| - In mathematics, a square number, sometimes also called 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. So, for example, 9 is a square number, since it can be written as 3 × 3. The usual notation for the formula for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name square number comes from the name of the shape. This is because a square with side length has area . Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number, is that its square root is again an integer. For example, , so 9 is a square number. A positive integer that has no perfect square divisors except 1 is called square-free. For a non-negative integer , the th square number is , with being the zeroth square. The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square (e.g., ). Starting with 1, there are square numbers up to and including , where the expression represents the floor of the number .
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