7 The least integer that is greater than $(2+\sqrt{3})^{2}$ is
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
7. Answer: (B)
$(2+\sqrt{3})^{2}=4+2 \sqrt{3}+3=7+2 \sqrt{3}$ and $(2-\sqrt{3})^{2}=7-2 \sqrt{3}$. So $(2+\sqrt{3})^{2}$ $+(2-\sqrt{3})^{2}=14$. Since $0<2-\sqrt{3}<1,0<(2-\sqrt{3})^{2}<1 \Rightarrow$ the least integer that is greater than $(2+\sqrt{3})^{2}$ is 14 .