$\begin{array}{l}\text{Here,}\\ \Rightarrow \text{\hspace{0.17em}(}\sqrt{8}\text{×}\sqrt{8}{\text{)}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\text{+}\sqrt{9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\text{) }={(?)}^3+\sqrt{8}-340\\ \\ \Rightarrow {\text{ (8)}}^{\frac{1}{2}}{\text{+ (9)}}^{\frac{1}{2}}{\text{= (?)}}^3\text{+}\sqrt{8}\text{-340}\\ \\ \begin{array}{l}\Rightarrow \sqrt{8}\text{+}\sqrt{9}\text{-}\sqrt{8}{\text{+340=(?)}}^3\\ \\ \Rightarrow (?{)}^3=343\end{array}\\ \\ \text{[taking cube root on both sides]}\\ \\ ?={}_{}{}^3\sqrt{343}=7\end{array}\text{}$

Hence, Option A is correct.