Answer: False
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Explanation:
Recall that the FOIL rule says
[tex](a+b)^2 = (a+b)(a+b) = a^2+2ab+b^2[/tex]
If we plug in [tex]a = \sqrt{2}[/tex] and [tex]b = \sqrt{3}[/tex], then you should find that
[tex](a+b)^2 = a^2+2ab+b^2\\\\(\sqrt{2}+\sqrt{3})^2 = (\sqrt{2})^2+2*\sqrt{2}*\sqrt{3}+(\sqrt{3})^2\\\\(\sqrt{2}+\sqrt{3})^2 = 2+2*\sqrt{2*3}+3\\\\(\sqrt{2}+\sqrt{3})^2 = 5+2\sqrt{6}\\\\[/tex]
So that 5 the student got is close, but there's a missing term needed to be added on: namely the [tex]2\sqrt{6}[/tex] term.
