The problem about \sqrt

Question

When the symbol in the \sqrt is too large, the \sqrt rendered in the article is too vertical and is not very beautiful. I want it to have a tilt angle, just like when there are few symbols inside. what should I do?

Answer 1

The fact that the steepness of the surds increases with the overall size of the square-root symbols is not a flaw in the design of the math font. Instead, it embodies a long-standing typographic tradition that has held up pretty well over the decades (and probably even centuries).

If you can't stand the "vertical look" of the taller surds, do contemplate some alternatives. Among them are (a) using \tfrac ("text style frac") rather than \frac; (b) using inline-fraction notation; (c) using reciprocal notation (e.g, 3^{-2} rather than \frac{1}{3^2}); and (d) parenthetic notation instead of \sqrt -- either with automatically sized parentheses or explicitly sized parentheses.

\documentclass{article}
\usepackage{amsmath} % for 'align*' env. and '\tfrac' and '\dotsb' macros
\usepackage{newpxtext,newpxmath} % Palatino clone

\begin{document}
\begin{align*}
c_n 
&= \sqrt{\frac{1}{3^2}+\sqrt{\frac{1}{4^2}+\sqrt{\dotsb+\frac{1}{n^2}}}}\\
&= \sqrt{\tfrac{1}{3^2}+\sqrt{\tfrac{1}{4^2}+\sqrt{\dotsb+\tfrac{1}{n^2}}}}\\
&= \sqrt{1/3^2+\sqrt{1/4^2+\sqrt{\dotsb+1/n^2}}}\\
&= \sqrt{3^{-2}+\sqrt{4^{-2}+\sqrt{\dotsb+\mathstrut n^{-2}}}}\\
&= \left(\frac{1}{3^2}+\left(\frac{1}{4^2}+\left(\dotsb+\frac{1}{n^2}
      \right)^{\!\!-1/2\,} \right)^{\!\!-1/2\,} \right)^{\!\!-1/2}\\
&= \Biggl(\frac{1}{3^2}+\biggl(\frac{1}{4^2}+\Bigr(\dotsb+\frac{1}{n^2}
      \Bigr)^{\!\!-1/2\,} \biggr)^{\!\!-1/2\,} \Biggr)^{\!\!-1/2}
\end{align*}

\end{document}