Which value among 11 + 5 ,\, 14 + 2 ,\, 8 + 8 is the largest?

Answer: Option C

$$\begin{array}{rl}& {\left(\sqrt{11}+\sqrt{5}\right)}^2=16+2\sqrt{55}\\ & {\left(\sqrt{14}+\sqrt{2}\right)}^2=16+2\sqrt{28}\\ & {\left(\sqrt{8}+\sqrt{8}\right)}^2=16+2\sqrt{64}\\ & \text{It is clear that }16+2\sqrt{64}\text{ is largest}\\ & \text{So, }\left(\sqrt{8}+\sqrt{8}\right)\text{ will be largest}\text{.}\end{array}$$