Let
Find the digit after the decimal point in the expression of \sqrt{m}
It seems a similar problem.
xkcd • View topic - math problem - driving me crazy
But I don't think so. I can't write m to a,b,n is integer numbers
No, I am not going to do that. It is too darn messy.
You can look up binomial series.
You might want to specifically look up the generalised binomial series since this has a fractional exponent. It's about 2/3 of the way down this page:
Binomial theorem - Wikipedia, the free encyclopedia