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In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of ...
In mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where x is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x is a number r (the root ...
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater ...
Use of Newton's method to compute square roots. Newton's method is one of many known methods of computing square roots. Given a positive number a, the problem of finding a number x such that x2 = a is equivalent to finding a root of the function f(x) = x2 − a. The Newton iteration defined by this function is given by.
Halley's method. In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's ...
Here the function is . In algebra, a cubic equation in one variable is an equation of the form. in which a is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation.
Secant method. In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years.
Digit-by-digit algorithm. The traditional pen-and-paper algorithm for computing the square root is based on working from higher digit places to lower, and as each new digit pick the largest that will still yield a square . If stopping after the one's place, the result computed will be the integer square root.