10. What is the value of
$$
(\sqrt{11}+\sqrt{5})^{8}+(\sqrt{11}-\sqrt{5})^{8} ?
$$
(A) 451856;
(B) 691962 ;
(C) 903712;
(D) 1276392;
(E) 1576392 .
10. Ans: (C)
We only need a rough estimate to rule out the wrong answers. $\sqrt{11} \approx 3.3$ and $\sqrt{5} \approx 2.2$, so the sum is $\approx 5.5^{8}+(1.1)^{8} \approx 5.5^{8}=30.25^{4} \approx 30^{4} \approx 810000$. Thus (C). Of course the exact answer can be obtained by calculations, for example,
$$
\begin{array}{l}
\sum_{i=0}^{8}\binom{8}{i}(\sqrt{11})^{i}(\sqrt{5})^{8-i}+\sum_{i=0}^{8}\binom{8}{i}(\sqrt{11})^{i}(-\sqrt{5})^{8-i} \\
=2 \sum_{i=\text { ex }}^{8}\binom{8}{i}(\sqrt{11})^{i}(\sqrt{5})^{8-i} \\
=2 \sum_{j=0}^{4}\binom{8}{2 j}(11)^{j}(5)^{4-j} .
\end{array}
$$