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A cube root of a number x is a number y such that y3 = x. Learn about the real and complex cube roots, their formal definition, geometric representation, numerical methods and applications in mathematics.
Newton's method, also known as the Newton–Raphson method, is a numerical technique to approximate the roots of a function. It uses the derivative of the function to construct a tangent line and find the x-intercept as a better approximation of the root.
Learn about different algorithms for approximating the non-negative square root of a positive real number, such as Heron's method, Newton's method, and continued fractions. Compare the accuracy, complexity, and history of various methods, and how to choose a suitable initial estimate.
An nth root of a number x is a number r that, when raised to the power of n, yields x. The number x is called the radicand and the index or degree of the root is n. Learn more about the history, notation, properties and operations of nth roots.
Learn about the origins and solutions of cubic equations, which are equations of the form ax3 + bx2 + cx + d = 0. Find out how ancient and medieval mathematicians from different cultures approached and solved cubic equations using algebra, geometry, and numerical approximations.
Learn about mental calculation, the arithmetical calculations using only the human brain, with no help from any supplies or devices. Find out the methods and techniques, such as casting out nines, factors, and FOIL, to perform mental calculations faster and more accurately.
Learn about the history, principles and methods of finding roots of polynomials, from linear to high degrees. Compare different algorithms, such as Newton's method, Francis QR algorithm, Aberth method and others.
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.