Two questions that weren't answered in the article:
1. How many digits of precision were required in the answer?
2. Was this an open ended question, as in the nth root of an x digit number, or did he know he would have to find the 13th root of a 20 digit number beforehand?
This is not a difficult problem for anyone with a math, science or engineering background. If all you need is 2 or 3 digits of precision, I'd expect any working scientist or similar to be able to do this in their head within a minute. In fact, if he knew he was going to be asked to take the 13th root of a 20 digit number and only needed two or three digits, I'd wonder why it took him so long. To make this notable, my guess is that he only knew that the question would be of the form "Find the nth root of an x digit number", and that he needed several digits of precision (like a half dozen).