sqrtNmF2

sqrtNmF2 is a compact symbolic expression used in certain mathematical and computational contexts to denote the principal square root of the product N m F^2. It is typically read as the square root of N times m times F squared.

Formally, sqrtNmF2 is defined as sqrt(N · m · F^2). Because F^2 is nonnegative for real F, the real-valued interpretation of sqrtNmF2 depends on the product N · m. In particular, when N · m ≥ 0 and F is real, sqrtNmF2 can be written as F · sqrt(Nm). More generally, sqrt(NmF^2) equals |F| · sqrt(Nm) for Nm ≥ 0; if Nm < 0 the result is complex.

Domain and value considerations: The expression yields a real value when Nm ≥ 0 and F is real; if Nm < 0, the value lies in the complex plane. The expression is monotone in |F| for fixed N and m, and scales linearly with |F| in that regime.

Usage and notes: This notation is not standard in conventional mathematics. In published work, it is common to write sqrt(N · m · F^2) or |F| · sqrt(Nm) to avoid ambiguity. When introducing sqrtNmF2, it is helpful to specify the underlying variables and the intended domain to prevent misinterpretation.

Example: With N = 9, m = 2, F = 3, sqrtNmF2 = sqrt(9 · 2 · 3^2) = sqrt(162) ≈ 12.73, equivalent to F · sqrt(Nm) = 3 · sqrt(18) ≈ 12.73.