# Square (algebra)

## Product of a number by itself / From Wikipedia, the free encyclopedia

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In mathematics, a **square** is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 3^{2}, which is the number 9.
In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations ` x^2` (caret) or

`may be used in place of`

*x***2`. The adjective which corresponds to squaring is`

*x*^{2}*quadratic*.

This article includes a list of general references, but it lacks sufficient corresponding inline citations. (August 2015) |

The square of an integer may also be called a *square number* or a *perfect square*. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial *x* + 1 is the quadratic polynomial (*x* + 1)^{2} = *x*^{2} + 2*x* + 1.

One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −*x*. That is, the square function satisfies the identity *x*^{2} = (−*x*)^{2}. This can also be expressed by saying that the square function is an even function.