Expand $(3+\sqrt{5})^4$. Enter your answer in the form $a + b\sqrt{5}$ for some positive integers $a$ and $b$.
By the Binomial Theorem
(3 + sqrt(5))^4
= 3^4 + C(5,1)*3^3*sqrt(5) + C(5,2)*3^2*sqrt(5)^2 + C(5,3)*3*sqrt(5)^3 + sqrt(5)^4
= 360 + 144*sqrt(5)
