$\newcommand{\cc}{\mathbb C}$ Let $R$ be a finitely generated $\cc$-algebra and ${\frak m}\subset R$ a maximal ideal. Denote by $\hat R$ the completion of $R$ with respect to $\frak m$. Assume that $x\in R^\times$ is a unit and let $\hat x$ denote the image of $x$ under $R\to\hat R$. I am wondering if $\hat x$ has an $n$-th root in $\hat R$, or in other words:
Is there an element $\xi\in\hat{R}$ such that $\xi^n = \hat x$?