2. The value of the algebraic expression $\sqrt{5-2 \sqrt{6}}+\sqrt{7-4 \sqrt{3}}$ is ( )
(A) $\sqrt{2}-2 \sqrt{3}+2$
(B) $2-\sqrt{2}$
(C) $2+2 \sqrt{3}-\sqrt{2}$
(D) $\sqrt{3}-\sqrt{2}$
Answer: (B)
Solution: Since
$$
5-2 \sqrt{6}=(\sqrt{3})^{2}-2 \times \sqrt{2} \times \sqrt{3}+(\sqrt{2})^{2}=(\sqrt{3}-\sqrt{2})^{2} \text {, }
$$

Since
$$
\sqrt{3}>\sqrt{2},
$$

Therefore
$$
\sqrt{5-2 \sqrt{6}}=\sqrt{3}-\sqrt{2}
$$

Similarly
$$
\sqrt{7-4 \sqrt{3}}=2-\sqrt{3} \text { . }
$$

Therefore
$$
\sqrt{5-2 \sqrt{6}}+\sqrt{7-4 \sqrt{3}}=\sqrt{3}-\sqrt{2}+2-\sqrt{3}=2-\sqrt{2} \text {. }
$$