The value of $$\frac{{2\sqrt {10} }}{{\sqrt 5 + \sqrt 2 - \sqrt 7 }} - \sqrt {\frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}} - \frac{3}{{\sqrt 7 - 2}}{\text{is:}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{{2\sqrt {10} }}{{\sqrt 5 + \sqrt 2 - \sqrt 7 }} - \sqrt {\frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}} - \frac{3}{{\sqrt 7 - 2}} \cr & = \frac{{2\sqrt {10} \left( {\sqrt 5 + \sqrt 2 + \sqrt 7 } \right)}}{{{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2} - {{\left( {\sqrt 7 } \right)}^2}}} - \sqrt {\frac{{{{\left( {\sqrt 5 - 2} \right)}^2}}}{{{{\left( {\sqrt 5 } \right)}^2} - {{\left( 2 \right)}^2}}}} - \frac{{3\left( {\sqrt 7 + 2} \right)}}{{{{\left( {\sqrt 7 } \right)}^2} - {{\left( 2 \right)}^2}}} \cr & = \frac{{2\sqrt {10} \left( {\sqrt 5 + \sqrt 2 + \sqrt 7 } \right)}}{{5 + 2 + 2\sqrt {10} - 7}} - \frac{{\left( {\sqrt 5 - 2} \right)}}{1} - \frac{{3\left( {\sqrt 7 + 2} \right)}}{3} \cr & = \sqrt 5 + \sqrt 2 + \sqrt 7 - \sqrt 5 + 2 - \sqrt 7 - 2 \cr & = \sqrt 2 \cr} $$