The value of $$\sqrt {28 + 10\sqrt 3 } - \sqrt {7 - 4\sqrt 3 } $$      is closest to:

Solution (By Examveda Team)

$$\eqalign{ & \sqrt {28 + 10\sqrt 3 } - \sqrt {7 - 4\sqrt 3 } \cr & = \sqrt {{{\left( {5 + \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} \cr & = 5 + \sqrt 3 - 2 + \sqrt 3 \cr & = 3 + 2\sqrt 3 \cr & = 3 + 2 \times 1.73 \cr & = 3 + 3.46 \cr & = 6.5 \cr} $$