The simplified value of (√3 + 1) (10 + $$\sqrt {12} $$ ) ($$\sqrt {12} $$ - 2) (5 - √3) is

Solution (By Examveda Team)

$$\eqalign{ & \left( {\sqrt 3 + 1} \right)\left( {10 + \sqrt {12} } \right)\left( {\sqrt {12} - 2} \right)\left( {5 - \sqrt 3 } \right) \cr & \Rightarrow \left( {\sqrt 3 + 1} \right)\left( {10 + 2\sqrt 3 } \right)\left( {2\sqrt 3 - 2} \right)\left( {5 - \sqrt 3 } \right) \cr & \Rightarrow \left( {\sqrt 3 + 1} \right) \times 2\left( {5 + \sqrt 3 } \right) \times 2\left( {\sqrt 3 - 1} \right)\left( {5 - \sqrt 3 } \right) \cr & \Rightarrow 4\left( {\sqrt 3 + 1} \right)\left( {\sqrt 3 - 1} \right)\left( {5 - \sqrt 3 } \right)\left( {5 + \sqrt 3 } \right) \cr & \Rightarrow 4\left( {3 - 1} \right)\left( {25 - 3} \right)\,\,\,\,\,\left[ {\left( {a + b} \right)\left( {a - b} \right) = {a^2} - {b^2}} \right] \cr & \Rightarrow 4 \times 2 \times 22 \cr & \Rightarrow 176 \cr & \therefore {\text{The required answer is }}176 \cr} $$