13. Which of these is the mean of the other four?
A $\sqrt{2}$
B $\sqrt{18}$
C $\sqrt{200}$
D $\sqrt{32}$
E $\sqrt{8}$
SolUTion
D
We use the fact that one of the options is the mean of the other four options provided that it is the mean of all five of the options. Your are asked to check this fact in Problem 13.2.
The mean of the five numbers given as options is
$$
\begin{aligned}
\frac{\sqrt{2}+\sqrt{18}+\sqrt{200}+\sqrt{32}+\sqrt{8}}{5} & =\frac{\sqrt{2}+3 \sqrt{2}+10 \sqrt{2}+4 \sqrt{2}+2 \sqrt{2}}{5} \\
& =\left(\frac{1+3+10+4+2}{5}\right) \sqrt{2} \\
& =\left(\frac{20}{5}\right) \sqrt{2} \\
& =4 \sqrt{2} \\
& =\sqrt{32} .
\end{aligned}
$$

Therefore the correct option is D.