13.13 The number closest to $\sqrt{65}-\sqrt{63}$ among the following is
(A) 0.12.
(B) 0.13.
(C) 0.14.
(D) 0.15.
(E) 0.16.
(38th American High School Mathematics Examination, 1987)
[Solution]
$$
\text { Given } \begin{aligned}
\sqrt{65}-\sqrt{63}= & \frac{(\sqrt{65}-\sqrt{63})(\sqrt{65}+\sqrt{63})}{\sqrt{65}+\sqrt{63}} \\
& =\frac{2}{\sqrt{65}+\sqrt{63}},
\end{aligned}
$$

Given $2 \sqrt{63} \approx 7.5$, then $15 < 2 \sqrt{a b} (a>b>0)$, we have $2(a+b)>a+b+2 \sqrt{a b}$, which means
$$
\sqrt{2(a+b)}>\sqrt{(\sqrt{a}+\sqrt{b})^{2}}=\sqrt{a}+\sqrt{b} \text {. }
$$

Therefore,
$$
\sqrt{63}+\sqrt{65}<\sqrt{2(63+65)}=2 \cdot 8=16 \text {, }
$$

Thus, $15<\sqrt{63}+\sqrt{65}<16$, then
$$
0.125=\frac{2}{16}<\sqrt{65}-\sqrt{63}<\frac{2}{15}=0.133 \cdots,
$$

Hence, the answer is $(B)$.