Square (math)

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 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"

{\ displaystyle 5 ^ {2} = 5 \ cdot 5 = 25}

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

{\ displaystyle 1 ^ {2} = 1; \; 2 ^ {2} = 4; \; 3 ^ {2} = 9; \; \ ldots}

However, squares can also be formed from any real or even complex numbers. More generally, the concept of the square can be applied to all internal two-digit relationships written in multiplicative terms, for example to the multiplication of matrices .

The function that each real number its square assigns, is square function and is one of the quadratic functions . Your 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 each number its square root . ${\ displaystyle x \ mapsto x ^ {2}}$ ${\ displaystyle x}$ ${\ displaystyle x ^ {2}}$ ${\ displaystyle x \ in \ mathbb {R} _ {0} ^ {+}}$ ${\ displaystyle {\ sqrt {x}}}$

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) opposite number: ${\ displaystyle (-a) ^ {2} = a ^ {2}}$

keyboard

On the German PC keyboard , the ² character is the third assignment on the 2 key and can be entered using the Alt-Gr key. You can often use the two keys Ctrl and Alt instead of Alt Gr . With an Apple keyboard, on the other hand, there is no defined key combination for the ² sign. The ² character and the code number (hexadecimal ) are part of the character coding ISO 8859-1 (or ISO 8859-15 ) and thus also the Unicode block Latin-1, supplement . 178B2

Square (math)

properties

keyboard

See also