Algebraic solution

do not have any algebraic solution. The same is true for every higher degree. However, for any degree there are some polynomial equations that have algebraic solutions; for example, the equation ${\displaystyle x^{10}=2}$ can be solved as ${\displaystyle x=\pm {\sqrt[{10}]{2}}.}$ The eight other solutions are nonreal complex numbers, which are also algebraic and have the form ${\displaystyle x=\pm r{\sqrt[{10}]{2}},}$ where r is a fifth root of unity, which can be expressed with two nested square roots. See also Quintic function § Other solvable quintics for various other examples in degree 5.