[Tex/LaTex] Nice-looking p-th roots

Question

When I take the pth root, the bottom of the p comes very close to the \sqrt symbol. In the New Century Schoolbook font (which I am using), the p actually intersects the \sqrt symbol, which looks even more terrible. Is there a clean way to fix this?

\documentclass{article}
\usepackage{fouriernc} % use the New Century Schoolbook font
\begin{document}
When I write $a^{(1/p)}$ as $\sqrt[p]{a}$, the bottom of the $p$
touches the top of the root symbol, which looks ugly.
Even when the root symbol is larger, such as with
$\sqrt[p]{\frac{1}{n}}$, it still looks bad
(since the tail of the p almost hits that line).
\end{document}

Answer 1

The amsmath package provides commands to tweak the position of the p, this example is from the amsmath documentation:

\sqrt[\leftroot{-2}\uproot{2}\beta]{k}