Editing Square root (section)

=={{mvar|n}}th roots and polynomial roots==

The definition of a square root of <math>x</math> as a number <math>y</math> such that <math>y^2 = x</math> has been generalized in the following way.

A [[cube root]] of <math>x</math> is a number <math>y</math> such that <math>y^3 = x</math>; it is denoted <math>\sqrt[3]x.</math>

If {{mvar|n}} is an integer greater than two, a [[Nth root|{{mvar|n}}-th root]] of <math>x</math> is a number <math>y</math> such that <math>y^n = x</math>; it is denoted <math>\sqrt[n]x.</math>

Given any [[polynomial]] {{math|''p''}}, a [[polynomial root|root]] of {{math|''p''}} is a number {{mvar|y}} such that {{math|1=''p''(''y'') = 0}}. For example, the {{mvar|n}}th roots of {{mvar|x}} are the roots of the polynomial (in {{mvar|y}}) <math>y^n - x.</math>

[[Abel–Ruffini theorem]] states that, in general, the roots of a polynomial of degree five or higher cannot be expressed in terms of {{mvar|n}}th roots.