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In algebra, the square of a number is that number multiplied by itself.

Its notation is a superscripted "2", thus a number x squared is written as x². Thus: $x^2 = x\times x$

If x is a positive real number, the value of x² is equal to the area of a square of edge length x.

A positive integer that is the square of some other integer, for example 25 which is 5², is known as a square number, or more simply a square.

The result of 0⁰ is not determined.

It is often also useful to note that the square of any number can be represented as the sum 1 + 1 + 2 + 2 + ... + n-1 + n-1 + n. For instance, the square of 4 or 4² is equal to 1 + 1 + 2 + 2 + 3 + 3 + 4 = 16. This is the result of adding a column and row of thickness 1 to the square graph of three (like a tic tac toe board). You add three to the side and four to the top to get four squared. This can also be useful for finding the square of a big number quickly. For instance, the square of 52 = 50² + 50 + 51 + 51 + 52 = 2500 + 204 = 2704.

Square (algebra)

See also