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

$(\sqrt{2} + \sqrt{3})^{2}$ equals
  1. $5 + 2\sqrt{6}$
  2. $5$
  3. $\sqrt{5}$
  4. $5\sqrt{6}$

Solution

$(a+b)^{2} = a^{2} + 2ab + b^{2} = 2 + 2\sqrt{6} + 3 = 5 + 2\sqrt{6}$.

Asked in: IMO

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