The number (\sqrt{2}+\sqrt{3})^3$ can be written in the form $a\sqrt{2} + b\sqrt{3} + c\sqrt{6}$, where $a$, $b$, and $c$ are integers. What is $a+b+c$?
\( (\sqrt{2}+\sqrt{3})^3\)
Using the binomial expansion we have
( √2)^3 + 3 ( √ 2)^2 (√3) + 3( √2)( √3)^2 + ( √3)^3 =
2 √2 + 6 √3 + 9 √2 + 3 √3 =
11 √2 + 9 √3 + 0 √6
So a + b + c = 11 + 9 + 0 = 20
