Square (algebra)

In mathematics, the square of a number is a calculation expression (term) that expresses the multiplication of this number by itself. The calculation of such a square is accordingly called squaring. A superscript two is used as a symbol for the square of a number.

Example: "5 (to the) square" or "5 to the power of 2".

The term "square" comes from geometry: A square in the geometric sense is a quadrilateral with four sides of equal length and four right angles. The area of such a square is calculated by multiplying the side length by itself.

The square of a number is a special case of a power, namely a power with the exponent 2.

The squares of the natural numbers are called square numbers:

However, squares of any real or even complex numbers can also be formed. More generally, the square notion can be applied to all multiplicatively written inner two-digit operations, for example to the multiplication of matrices.

The function which assigns to each real number its square called a quadratic function and belongs to the quadratic functions. Its graph is the so-called normal parabola. The inverse function of the square function restricted to non-negative real numbers is the (square) root function, which assigns to each number its square root .

Properties

• For properties of the square of natural numbers, see square number.
• The square of a negative number is always the square of its (positive) counterpart:

Keyboard

On the German PC keyboard, the ² character is located as the third assignment on the 2 key and can be entered with the help of the Alt-Gr key. Often you can also use the two keys Ctrl and Alt instead of Alt Gr. On an Apple keyboard, however, there is no defined key combination for the ² character. With the code number 178 (hexadecimal B2), the ² character is part of the character encoding ISO 8859-1 (or ISO 8859-15) and thus also of the Unicode block Latin-1, Supplement.

See also