+40 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 $a+b+c$?
Expanding the binomial theorem, we get (sqrt(2) + sqrt(3))^3 = 15*sqrt(2) + 8*sqrt(3). So a + b + c = 15 + 8 + 0 = 23.
+40 Not to be rude but those two sides of the equation aren't equal. The first one is equal to around 31 and the second is equal to around 35.
