# existence of nth root

If $n$ is a positive integer and $a>0$ then the polynomial $x^{n}-a\in\mathbb{R}[x]$ has one sign change so by Descartes’s Rule of Signs has a unique positive real root.

Title existence of nth root ExistenceOfNthRoot1 2013-03-22 16:08:38 2013-03-22 16:08:38 Mathprof (13753) Mathprof (13753) 10 Mathprof (13753) Proof msc 26C10 msc 12D99 msc 26A06 ExistenceOfRoot ExistenceOfSquareRootsOfNonNegativeRealNumbers