Is there a way to get higher-root symbols to render correctly when rooting a fraction?

Question

Given a root symbol that becomes tall:

$$\sqrt[N]{\dfrac{\lambda}{3^e}}$$

The N is now rendered disproportionately small.

Does a fix exist? Is this a bug?

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edit: as a follow-up to the accepted answer, here is a reference on font size and style setting

Answer 1

You could try

text{\sqrt[\large N]{\dfrac{\lambda}{3^e}}: $\quad\displaystyle\sqrt[\large N]{\dfrac{\lambda}{3^e}}$

or text{\sqrt[\Large N]{\dfrac{\lambda}{3^e}}: $\quad\displaystyle\sqrt[\Large N]{\dfrac{\lambda}{3^e}}$

but \sqrt[\huge N]{\dfrac{\lambda}{3^e}}: $\quad\displaystyle\sqrt[\huge N]{\dfrac{\lambda}{3^e}}$

starts to look very odd.

Afterthought:

I was looking at the larger indices and they looked kind of crowded to the radical. I think these look even better:

text{\sqrt[\raise{2pt}{\large N}]{\dfrac{\lambda}{3^e}}: $\quad\displaystyle\sqrt[\raise{2pt}{\large N}]{\dfrac{\lambda}{3^e}}\quad\Large\star$

or text{\sqrt[\raise{2pt}{\Large N}]{\dfrac{\lambda}{3^e}}: $\quad\displaystyle\sqrt[\raise{2pt}{\Large N}]{\dfrac{\lambda}{3^e}}$

I think the starred one looks best