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 $a+b+c$?
\((\sqrt{2}+\sqrt{3})^3\) ⇒ \( a\sqrt{2} + b\sqrt{3} + c\sqrt{6}\)
( √2 + √3)^3 =
(√2)^3 + 3*(√2)^2 *(√3) + 3 * (√2) *(√3)^2 + ( √3)^3 =
2√2 + 3*2*√3 + 3*3*√2 + 3√3 =
2√2 + 9√2 + 6√3 + 3√3 =
11√2 + 9 √3 + 0 √6
a + b + c =
11 + 9 + 0 =
20
