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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.
Learn what a square root is, how to write it, and how to find it for any number. Explore the history of square roots from ancient times to modern mathematics, and the properties and uses of the square root function.
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.
An nth root of a number x is a number r that, when raised to the power of n, yields x. Learn about the notation, history, arithmetic operations and identities of nth roots, especially square roots and cube roots.
Learn about the square root of 2, a positive real number that equals the length of a diagonal across a square with sides of one unit. Find out its history, representations, decimal value, and algorithms.
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.
The square root of 7 is the positive real number that, when multiplied by itself, gives the prime number 7. It is an irrational algebraic number that has a decimal expansion that never ends or repeats, and can be approximated by rational numbers using continued fractions or Newton's method.
Learn about the irrational number that is the positive solution of x2 = 5, and its relation to the golden ratio, Fibonacci numbers, and geometry. Find its decimal expansion, continued fraction, rational approximations, and trigonometric formulae.