sqrtLgbx

sqrtLgbx is a notational convention used to denote the principal square root of the product of four parameters L, g, b, and x. It is defined by the relation sqrtLgbx = sqrt( L * g * b * x ). The meaning of the square root follows the standard conventions for real and complex numbers.

Domain and value range

When L, g, b, and x are real and their product L*g*b*x is nonnegative, sqrtLgbx is a nonnegative real number. If the product is negative or if complex values are involved, sqrtLgbx refers to the principal square root in the complex plane, with the usual branch cut along the negative real axis.

Notation and interpretation

The name sqrtLgbx reflects the four factors that commonly appear together in certain mathematical models or formulas. It is used primarily as shorthand in contexts where L, g, b, and x appear multiplicatively and are grouped as a single factor.

Properties

For nonnegative real inputs, sqrtLgbx = sqrt(L g b x) and, when each factor is nonnegative, sqrtLgbx = sqrt(L) sqrt(g) sqrt(b) sqrt(x). In general, however, sqrt(u v) cannot be separated into independent square roots when complex numbers are involved, so one should treat sqrtLgbx as the single square root of the product.

Computation and examples

Numerically, compute p = L*g*b*x and then take the square root of p. For example, L=4, g=2, b=3, x=1 yields sqrtLgbx = sqrt(24) ≈ 4.898979.