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Methods of computing square roots are algorithms for approximating 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 methods typically construct a series of increasingly accurate approximations .
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. That formula always gives the roots ...
The process of simplifying expressions involving the square root of an expression involving the square root of another expression involves finding the two solutions of a quadratic equation.
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 .
Rationalisation (mathematics) In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated. If the denominator is a monomial in some radical, say with k < n, rationalisation consists of multiplying the numerator and the denominator by and replacing by x (this is allowed ...
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula (in some countries referenced as Bhaskara's formula) is a closed-form expression describing ...
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 .
Clearing denominators. In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions .