Expand and simplify $(2 + \sqrt{5})^2$.
A$9 + 2\sqrt{5}$
B$4 + 5\sqrt{2}$
C$29$
D$9 + 4\sqrt{5}$CORRECT
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Why the answer is D, and why the others tempt you.
Use $(a+b)^2 = a^2 + 2ab + b^2$: $4 + 2(2)(\sqrt{5}) + 5 = 9 + 4\sqrt{5}$. Halving the middle term gives $9 + 2\sqrt{5}$, and treating $(\sqrt{5})^2$ as 25 gives 29.
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