The expression $$\sqrt {10 + 2\left( {\sqrt 6 - \sqrt {15} - \sqrt {10} } \right)} $$      is equal to:

$$\eqalign{ & \sqrt {10 + 2\left( {\sqrt 6 - \sqrt {15} - \sqrt {10} } \right)} \cr & = \sqrt {{{\left( {\sqrt 2 } \right)}^2} + {{\left( {\sqrt 3 } \right)}^2} + {{\left( { - \sqrt 5 } \right)}^2} + 2\left( {\sqrt 2 \times \sqrt 3 - \sqrt 3 \times \sqrt 5 - \sqrt 5 \times \sqrt 2 } \right)} \cr & = \sqrt {{{\left( {\sqrt 2 + \sqrt 3 - \sqrt 5 } \right)}^2}} \cr & = \sqrt 2 + \sqrt 3 - \sqrt 5 \cr} $$