sqrtR

sqrtR is a notation used in some mathematical and computational contexts to denote the square root of a quantity R. It is equivalent to the standard sqrt(R) when R is nonnegative, and is often used to emphasize the dependence on the variable R in formulas or algorithms.

In real arithmetic, sqrtR denotes the principal (nonnegative) square root. This means that for any real R with R ≥ 0, sqrtR is the unique real number x such that x^2 = R and x ≥ 0. For R < 0, the real square root is not defined. In complex arithmetic, square roots come in pairs, and sqrtR may refer to one of the two values, typically the principal value is chosen by convention, but the expression can have two complex roots ±√|R| i.

In programming and applied mathematics, sqrtR is sometimes used as a variable name or function shorthand to highlight the input R. Most programming languages provide a standard sqrt function that returns the principal square root of its argument. When R is a symbol for a physical quantity like a radius, sqrtR can appear in formulas where a square-root scaling is relevant, but the term itself is context-dependent and not a universal mathematical symbol.

Key properties include (sqrtR)^2 = R for R ≥ 0, and sqrtR ≥ 0 by definition. For nonnegative R, the product rule sqrt(R1 R2) = sqrt(R1) sqrt(R2) holds when R1 and R2 are nonnegative, with caution in mixed-sign or complex cases.

Examples: sqrtR with R = 16 yields 4; with R = 0 yields 0; with R = 2 yields approximately 1.41421356.