Kvadratrot

Kvadratrot, in English known as the square root, is the inverse operation of squaring. For a nonnegative real number x, the kvadratrot √x is the unique nonnegative number y such that y^2 = x. It is the principal square root and is denoted by the radical sign √.

In the real numbers, the domain of the kvadratrot is x ≥ 0, and the range is y ≥ 0. Fundamental properties include √(a^2) = |a| for any real a, and for nonnegative a and b the product rule √(ab) = √a · √b. The kvadratrot function is increasing on [0, ∞). It serves as the inverse of the squaring function on the nonnegative reals.

In the complex plane, every nonzero complex number z has two square roots. A common convention is to define a principal square root using the principal value of the complex logarithm, giving √z = exp(½ Log z). Without choosing a branch, the square root function is multivalued.

Computationally, many square roots are irrational (for example, √2). They often lack a finite or repeating decimal expansion and are approximated numerically by methods such as Newton–Raphson.

Applications of kvadratrot appear across mathematics and applied sciences: in geometry for right triangles and the Pythagorean theorem, in solving quadratic equations, in physics and engineering, and in numerical analysis and statistics. The symbol √ and the concept of a square root have a long history in mathematics, with the term kvadratrot used in Swedish and Norwegian.