sqrtqab

sqrtqab is a notation encountered in mathematics that is typically read as the square root of the product qab, i.e., sqrt(qab). The exact meaning can depend on context, and without parentheses the expression can be ambiguous; most authors clarify by writing sqrt(qab) or (sqrt q) ab when appropriate.

Definition and domain. For real numbers q, a, b, sqrtqab usually denotes the nonnegative real number whose square is qab, provided qab is nonnegative. If qab < 0 and complex numbers are allowed, sqrtqab is understood as the principal square root in the complex plane, often involving an imaginary unit.

Algebraic properties. When q, a, and b are nonnegative reals, sqrt(qab) = sqrt(q) sqrt(a) sqrt(b) if each factor is treated under a radical separately. In general, the rule sqrt(xy) = sqrt(x) sqrt(y) holds for nonnegative x and y; caution is required when any factor may be negative or when working in complex numbers. If any of q, a, or b is zero, sqrtqab equals zero.

Examples. sqrt(2*3*4) = sqrt(24) = 2 sqrt(6). If qab = -9, the real-valued square root is not defined; in complex arithmetic, sqrt(-9) = 3i.

Applications. The expression arises in contexts where a common multiplicative factor is under a radical, such as normalization constants, weighting factors, or energy-like quantities in physics, and in various algebraic simplifications involving products under a square root.

See also. square root, radical, product rule.