The only solution I can think of is to use the binomial theorem (http://en.wikipedia.org/wiki/Binomial_theorem) to expand (3+sqrt(5))^n . Then you only need to take into the account the terms where y (sqrt(5)) has an odd power because all others are integers and won't affect the decimals. Then after adding them up you'll end up with something like n * sqrt(5) where n is the total of the coeficients of sqrt(5) and then just do the math and find out the 3 decimals.
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