Mathsqrt

Mathsqrt is a term used to denote the operation of extracting a square root in both mathematical notation and programming libraries. It corresponds to the nonnegative number y such that y squared equals x, with the conventional square root symbol denoting the principal square root, written as √. In real arithmetic, the square root function, commonly written sqrt(x) or x^(1/2), is defined for nonnegative x and yields a nonnegative result. It is the inverse of the squaring function on the domain [0, ∞).

Key properties include sqrt(xy) = sqrt(x) sqrt(y) for nonnegative x and y, and sqrt(x^2) = |x|. The function is increasing on [0, ∞), and its graph is the smooth, concave curve starting at (0,0) that grows without bound as x increases. In complex analysis, every nonzero x has two square roots, and a principal branch is often defined by a chosen cut in the complex plane.

In programming contexts, the square root is typically implemented as a function in a math library, often named sqrt or Math.sqrt. Examples include Python's math.sqrt, JavaScript's Math.sqrt, and C's sqrt function in math.h. For negative inputs in real-number environments, many languages raise a domain error or return NaN, while some provide complex-number variants that return a complex result. Implementations may use efficient numerical methods, such as Newton-Raphson, to compute the result with good precision and performance.