In mathematics, a square root of a number a is a number y such that y2 = a, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16.
Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by √, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, denoted √ = 3, because 32 = 3 × 3 = 9 and 3 is non-negative. The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.
In numerical analysis, a branch of mathematics, there are several square root algorithms or methods for calculating the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below.
Finding is the same as solving the equation . Therefore, any general numerical root-finding algorithm can be used. Newton's method, for example, reduces in this case to the so-called Babylonian method:
In mathematics, a half iterate (sometimes called a functional square root) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x. For example, f(x) = 2x2 is a functional square root of g(x) = 8x4. Similarly, the functional square root of the Chebyshev polynomials g(x) = Tn(x) is f(x) = cos (√n arccos(x)), in general not a polynomial.
Notations expressing that f is a functional square root of g are f = g[½] and f = g½.
Hospitality is the relationship between the guest and the host, or the act or practice of being hospitable. This includes the reception and entertainment of guests, visitors, or strangers.
The word hospitality derives from the Latin hospes, meaning "host", "guest", or "stranger". Hospes is formed from hostis, which means "stranger" or "enemy" (the latter being where terms like "hostile" derive).