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Expand \((\sqrt{2} + \sqrt{3} + \sqrt{6})^2\) 

I think I combine some term, but I'm not sure.

 Jun 30, 2020
 #1
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\((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)

 

just plug in the values and solve!

 

\((\sqrt{2})^2+(\sqrt{3})^2+(\sqrt{6})^2+2(\sqrt{2}\cdot\sqrt{3})+2(\sqrt{3}\cdot\sqrt{6})+2(\sqrt{2}\cdot\sqrt{6})\)

\(=2+3+6+2\sqrt{6}+2\sqrt{18}+2\sqrt{12}\)

\(=11+2\sqrt{6}+2\sqrt{18}+2\sqrt{12}\)

\(=11+2\sqrt{6}+2\sqrt{9\cdot2}+2\sqrt{3\cdot4}\)

\(=\boxed{11+2\sqrt{6}+6\sqrt{2}+4\sqrt{3}}\)

 Jun 30, 2020

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