In the number $(1+\sqrt{3})^{2015}$, what is the 224th digit after the decimal point?
You may NOT use a calculator, computer, or any electronic aid to answer this question. Only pen(cil), paper, and brain are allowed.
This should be relatively easy, but it's a puzzle of a kind I haven't seen on this site before, and hopefully it'll set a trend for puzzles that are the opposite of computer-puzzle ones!