Finding certain digits of constructible irrational numbers.

Question

Let $n\neq m^q$ and $round(\sqrt[q]{n})=m$ for some $\{m,n,q\}\in\mathbb{N}$. Then, is there any way to find the $n^r$th digit of $\sqrt[q]{n}$, for $r\in\mathbb{N}$? I once saw something about someone claiming to know the $2^{2020}$th digit of $\sqrt2$, so I'm curious now. However, I myself have no idea how to ever find the digit.

Answer 1

You can find a method for calculating every digit of $\sqrt[q]{n}$ at this link:

https://en.wikipedia.org/wiki/Nth_root#Computing_principal_roots