How many digits of an $n$ digit positive integer do I need to know to correctly guess the first $m$ digits of the $k$ th root of $n$.

Question

Please help me solve this puzzle, which in my opinion only sounds tough:

How many digits (counting from the left) of an $n$ digit positive integer do I need to know to correctly guess the first $m$ digits of the $k$th ($k \geq 1$) root of $n$.