sqrt1

sqrt1 is not a standard standalone term in mathematics, but it is commonly understood as the square root of 1, written as sqrt(1) or √1. The square root symbol denotes the principal, nonnegative root of a nonnegative number.

For the real numbers, the principal square root of 1 equals 1. In contrast, the equation x^2 = 1 has two solutions, x = 1 and x = -1, since both numbers square to 1. The sqrt function, by convention, returns the nonnegative root, so sqrt(1) = 1.

In the broader context of complex numbers, every nonzero number has two square roots. For the complex plane, the principal square root is chosen by a convention (often the one with nonnegative real part), which for the number 1 yields the root 1. Thus, while 1 has two square roots, the principal square root of 1 remains 1.

Key properties related to the square root operation include the domain restriction that real-valued sqrt(a) is defined only for a ≥ 0 and the multiplicative rule sqrt(ab) = sqrt(a) sqrt(b) when a and b are nonnegative. The value sqrt(1) = 1 also aligns with the identity 1^0.5 = 1.

See also: square root, quadratic equation, exponents, complex square roots.