Editing Algebraic number (section)

===Numbers defined by radicals===
Any number that can be obtained from the integers using a [[finite set|finite]] number of [[addition]]s, [[subtraction]]s, [[multiplication]]s, [[division (mathematics)|division]]s, and taking (possibly complex) {{mvar|n}}th roots where {{mvar|n}} is a positive integer are algebraic. The converse, however, is not true: there are algebraic numbers that cannot be obtained in this manner. These numbers are roots of polynomials of degree&nbsp;5 or higher, a result of [[Galois theory]] (see [[Quintic equation]]s and the [[Abel–Ruffini theorem]]). For example, the equation:

:<math>x^5-x-1=0</math>

has a unique real root, ≈ 1.1673, that cannot be expressed in terms of only radicals and arithmetic operations.