sqrtxy2
sqrtxy2 is not a widely recognized mathematical symbol. In text without punctuation, it most plausibly denotes the expression sqrt(x y^2), i.e., the square root of the product x times y squared, though other interpretations may occur depending on context. When dealing with real variables, the radicand x y^2 is nonnegative if and only if x ≥ 0, since y^2 ≥ 0 for all real y. Under this condition, sqrt(x y^2) simplifies to sqrt(x) sqrt(y^2) = sqrt(x) |y|. Consequently, if x ≥ 0 and y ≥ 0, sqrt(x y^2) reduces to y sqrt(x); if y < 0, it reduces to -y sqrt(x). If x < 0, the radicand is negative and the real square root is undefined; in the complex domain, sqrt(x y^2) is defined but becomes multivalued.
Examples: x=9, y=-4 gives sqrt(9*16) = 12, consistent with |y| sqrt(x) = 4*3 = 12.
In programming and computer algebra systems, sqrt(x*y^2) is often written as sqrt(x)*abs(y) or sqrt(x*y^2) with the
See also: square root, absolute value, radicand, simplification of radicals, real numbers, complex numbers.