sqrtRR

sqrtRR is a term encountered in some mathematical texts and software libraries to denote the square root operation on the real numbers, often realized as a function named sqrtRR within a module or namespace that handles real (RR) values. It is not a universally standardized symbol; the conventional notation for this operation is sqrt, or Real.sqrt in programming environments.

In mathematical terms, sqrtRR(x) yields the nonnegative real y such that y^2 = x, for all x in the domain x ≥ 0. In the context of the real numbers, negative inputs do not have real square roots, so sqrtRR is undefined for x < 0 within the real number system. When complex numbers are allowed, the square root is extended to include both branches, with the principal square root typically chosen by convention.

From a computational perspective, implementations of sqrtRR must handle domain errors for negative inputs, potentially raise exceptions, or return a defined special value. In floating-point arithmetic, care is taken to manage rounding errors and to preserve monotonicity on [0, ∞). Some libraries also offer robust variants, such as interval-based or extended-precision versions, that provide bounds for sqrt(x) when the input may be uncertain.

Notationally, the exact meaning of sqrtRR can vary by language or library. When encountered, it is advisable to consult the surrounding documentation to confirm what RR stands for (often the real numbers) and how inputs outside the domain are handled. See also square root, real numbers, principal square root, and interval arithmetic.