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0
128
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Expand $(3+\sqrt{5})^4$. Enter your answer in the form $a + b\sqrt{5}$ for some positive integers $a$ and $b$.

Aug 9, 2021

#1
0

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)

Aug 9, 2021