Which value among $$\sqrt {11} + \sqrt 5 ,\,\sqrt {14} + \sqrt 2 ,\,\sqrt 8 + \sqrt 8 $$      is the largest?

Solution (By Examveda Team)

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