sqrtss3

sqrtss3 is a term used in mathematics and computer science to denote an operation that returns the square root of the sum of the squares of three numbers. In many contexts, it is equivalent to the Euclidean norm or L2 norm of a three-dimensional vector (a, b, c), i.e., sqrt(a^2 + b^2 + c^2).

Formally, for real numbers a, b, c, sqrtss3(a, b, c) = sqrt(a^2 + b^2 + c^2). Since squares are nonnegative, the result is always nonnegative.

Example: sqrtss3(3, 4, 12) = sqrt(9 + 16 + 144) = sqrt(169) = 13.

Generalizations extend the idea to higher dimensions and are often written as sqrtssN for N components, or more commonly as the L2 norm ||v||_2 = sqrt(sum xi^2). Some programming languages provide built-in functions to compute these values with improved numerical stability.

Implementation notes: use floating-point types to avoid overflow for large inputs; for numerical stability, use stable functions such as hypot when available, or techniques that reduce rounding errors in the sum of squares. If any component is negative, squaring eliminates the sign.

See also: Euclidean norm, L2 norm, hypot, vector magnitude, Pythagorean theorem.