The simplified value of $$\left( {\sqrt 6 + \sqrt {10} - \sqrt {21} - \sqrt {35} } \right)\left( {\sqrt 6 - \sqrt {10} + \sqrt {21} - \sqrt {35} } \right){\text{is}}$$

Solution (By Examveda Team)

$$\eqalign{ & \left( {\sqrt 6 + \sqrt {10} - \sqrt {21} - \sqrt {35} } \right)\left( {\sqrt 6 - \sqrt {10} + \sqrt {21} - \sqrt {35} } \right) \cr & = \left\{ {\left( {\sqrt 6 - \sqrt {35} } \right) + \left( {\sqrt {10} - \sqrt {21} } \right)} \right\}\left\{ {\left( {\sqrt 6 - \sqrt {35} } \right) - \left( {\sqrt {10} - \sqrt {21} } \right)} \right\} \cr & = {\left( {\sqrt 6 - \sqrt {35} } \right)^2} - {\left( {\sqrt {10} - \sqrt {21} } \right)^2} \cr & = \left( {6 - 35 - 2\sqrt {210} } \right) - \left( {10 + 21 - 2\sqrt {210} } \right) \cr & = 41 - 2\sqrt {210} - 31 + 2\sqrt {210} \cr & = 41 - 31 \cr & = 10 \cr} $$