Methods of computing square roots | square root expansion
AlgorithmsforcalculatingsquarerootsMethodsofcomputingsquarerootsarenumericalanalysisalgorithmsforfindingtheprincipal,ornon-negative,squareroot(usuallydenoted√S,2√S,orS1/2)ofarealnumber.Arithmetically,itmeansgivenS,aprocedureforfindinganumberwhichwhenmultipliedbyitself,yieldsS;algebraically,itmeansaprocedureforfindingthenon-negativerootoftheequationx2-S=0;geometrically,itmeansgiventheareaofasquare,aprocedureforconstructingasideofthesquare.Everyrealnumberhastwosquareroots.[Note1]Theprincipalsq...
Algorithms for calculating square roots
Methods of computing square roots are numerical analysis algorithms for finding the principal, or non-negative, square root (usually denoted √S, 2√S, or S1/2) of a real number. Arithmetically, it means given S, a procedure for finding a number which when multiplied by itself, yields S; algebraically, it means a procedure for finding the non-negative root of the equation x2 - S = 0; geometrically, it means given the area of a square, a procedure for constructing a side of the square.
Every real number has two square roots.[Note 1] The principal square root of most numbers is an irrational number with an infinite decimal expansion. As a result, the decimal expansion of any such square root can only be computed to some finite-precision approximation. However, even if we are taking the square root of a perfect square integer, so that the result does have an exact finite representation, the procedure used to compute it may only return...