Well for growth above 10% it's indeed tricky mathematically and there is no easy trick as most approximation fall short once you're not close to zero anymore but let's think about it logically will you.
If i call x the CAGR and n the number of year i consider I have to compute (1+x)^n.
To first order it is roughly equal to 1+n*x and to second order to 1+n*x+n*(n-1)/2*x^2.
Let's go with five years (so n=5).
For a CAGR of 5% by using the first approximation you'll do an error of 2.0%. And an error of 0.1% by using the second one.
For a CAGR of 10% the error will be 6.9% and 0.6%
For a CAGR of 20% it will be 19.6% and 3.5%.
This is perfectly fine to have an error of 3.5%. So if you ran into such a question during an actual interview (only happened to me twice once in a prep case and once in actual interview) just go with the first order approximation and do the second order one once the CAGR is above 10%. This seems to be something you can run into during cases for companies that do a lot of due dill.
And if the interviewer ask what is the error will be (which will never happen) it's easy as it will be on the order of the next leading term.
(edited)