$$\sqrt {8 - 2\sqrt {15} } $$   is equal to = ?

$$\eqalign{ & \sqrt {8 - 2\sqrt {15} } \cr & = \sqrt {5 + 3 - 2 \times \sqrt 5 \times \sqrt 3 } \cr & = \sqrt {{{\left( {\sqrt 5 } \right)}^2} + {{\left( {\sqrt 3 } \right)}^2} - 2 \times \sqrt 5 \times \sqrt 3 } \cr & = \sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} \cr & = \left( {\sqrt 5 - \sqrt 3 } \right) \cr} $$