7. The positive integer $k$ satisfies the equation $\sqrt{2}+\sqrt{8}+\sqrt{18}=\sqrt{k}$. What is the value of $k$ ?
A 28
B 36
C 72
D 128
Solution
C
Because $8=2^{2} \times 2$ and $18=3^{2} \times 2$, we have $\sqrt{8}=2 \sqrt{2}$ and $\sqrt{18}=3 \sqrt{2}$. Therefore
$$
\begin{aligned}
\sqrt{2}+\sqrt{8}+\sqrt{18} & =\sqrt{2}+2 \sqrt{2}+3 \sqrt{2} \\
& =6 \sqrt{2} \\
& =\sqrt{6^{2} \times 2} \\
& =\sqrt{72}
\end{aligned}
$$

Therefore $k=72$.