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 $a+b+c$?

\( (\sqrt{2}+\sqrt{3})^3\)

\(a\sqrt{2} + b\sqrt{3} + c\sqrt{6} \)

We just have a binomial expansion .....

( √2)^3 + 3(√2)^2(√3) + 3(√2)(√3)^2 + (√3)^3 simplify

2√2 + 6√3 + 9√2 + 3√3 =

11√2 + 9√3 + 0√6

So.....a + b + c = 20