Expand \((\sqrt{2} + \sqrt{3} + \sqrt{6})^2\)
I think I combine some term, but I'm not sure.
+738 \((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
just plug in the values and solve!
\((\sqrt{2})^2+(\sqrt{3})^2+(\sqrt{6})^2+2(\sqrt{2}\cdot\sqrt{3})+2(\sqrt{3}\cdot\sqrt{6})+2(\sqrt{2}\cdot\sqrt{6})\)
\(=2+3+6+2\sqrt{6}+2\sqrt{18}+2\sqrt{12}\)
\(=11+2\sqrt{6}+2\sqrt{18}+2\sqrt{12}\)
\(=11+2\sqrt{6}+2\sqrt{9\cdot2}+2\sqrt{3\cdot4}\)
\(=\boxed{11+2\sqrt{6}+6\sqrt{2}+4\sqrt{3}}\)
