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- Square root algorithms - Wikipedia
Square root algorithms compute the non-negative square root of a positive real number Since all square roots of natural numbers, other than of perfect squares, are irrational, [1] square roots can usually only be computed to some finite precision: these algorithms typically construct a series of increasingly accurate approximations
- Square root - Wikipedia
Notation for the (principal) square root of x For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 52 (5 squared) In mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x [1] For example, 4 and −4 are square roots of 16 because Every nonnegative real number x has a unique
- Pells equation - Wikipedia
A general development of solutions of Pell's equation in terms of continued fractions of can be presented, as the solutions x and y are approximates to the square root of n and thus are a special case of continued fraction approximations for quadratic irrationals
- Nested radical - Wikipedia
One has two nested square roots with an expression of the form where all variables denote rational numbers By rationalizing the fraction, one gets an expression of the form where are rational numbers and
- Solving quadratic equations with continued fractions - Wikipedia
Solving quadratic equations with continued fractions In mathematics, a quadratic equation is a polynomial equation of the second degree The general form is where a ≠ 0 The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square
- Integer square root - Wikipedia
Integer square root In number theory, the integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of n, For example,
- nth root - Wikipedia
Modern notation for the n th root of the variable x In mathematics, an nth root of a number x is a number r which, when raised to the power of n, yields x: The positive integer n is called the index or degree, and the number x of which the root is taken is the radicand A root of degree 2 is called a square root and a root of degree 3, a cube root Roots of higher degree are referred by using
- Square root of 2 - Wikipedia
Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem It was probably the first number known to be irrational [1] The fraction 99 70 (≈ 1 4142 857) is sometimes used as a good rational approximation with a reasonably small denominator
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