Square Root | square root definition
Asquarerootofisanumbersuchthat.Whenwrittenintheformorespecially,thesquarerootofmayalsobecalledtheradical[1]orsurd[2].Thesquarerootisthereforeannthroot[3]with.Notethatanypositiverealnumberhastwosquareroots,onepositiveandonenegative.Forexample,thesquarerootsof9areand,since.Anynonnegativerealnumberhasauniquenonnegativesquareroot;thisiscalledtheprincipalsquareroot[4]andiswrittenor.Forexample,theprincipalsquareroot[5]of9is,whiletheothersquarerootof9is.Incommonusage,unlessotherwisespecified,"the"s...
A square root of is a number such that . When written in the form or especially , the square root of may also be called the radical[1] or surd[2]. The square root is therefore an nth root[3] with .
Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are and , since . Any nonnegative real number has a unique nonnegative square root ; this is called the principal square root[4] and is written or . For example, the principal square root[5] of 9 is , while the other square root of 9 is . In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root. The principal square root function is the inverse function[6] of for .
Any nonzero complex number[7] also has two square roots. For example, using the imaginary unit[8] i, the two square roots of are . Th...