kvadrerade

Kvadrerade is Swedish for “squared.” Det is the past participle of kvadrera and can function as an adjective meaning that a quantity has been raised to the second power. The corresponding verb forms include kvadrera (to square) and kvadreras (is squared).

In mathematics, kvadrering is the operation of raising a number to the power of two. Denotation is commonly written as x^2 or x·x. For example, 3 kvadrerad blir 9, and (−4)^2 equals 16. The operation follows rules such as (ab)^2 = a^2 b^2 and (a+b)^2 = a^2 + 2ab + b^2.

Kvadrerade tal, or perfect squares, are the integers of the form n^2 where n is an integer. The sequence begins 0, 1, 4, 9, 16, 25, and so on. Kvadrering yields nonnegative results, and the last digits of squares follow specific patterns in modular arithmetic.

Outside pure math, kvadrering appears in statistics and data analysis in the form of squared quantities, such as squared residuals or the sum of squares used to quantify deviations from a model. These squared values emphasize larger deviations and are central to many optimization and fitting procedures.

Etymology and related terms: kvadrera derives from kvadrat, meaning square, with roots in Latin quadratus. Related Swedish terms include kvadrat (the geometric square) and kvadrering (the act of squaring).