$\begin{array}{l} E = 2\sqrt {4 + \sqrt {6 - 2\sqrt 5 } } .\left( {\sqrt {10} - \sqrt 2 } \right)\\ E = 2\sqrt {4 + \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} } \left( {\sqrt {10} - \sqrt 2 } \right)\\ E = 2\sqrt {3 + \sqrt 5 } .\left( {\sqrt 5 - 1} \right).\sqrt 2 \\ E = 2\sqrt {6 + 2\sqrt 5 } .\left( {\sqrt 5 - 1} \right)\\ E = 2\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} .\left( {\sqrt 5 - 1} \right)\\ E = 2\left( {\sqrt 5 + 1} \right)\left( {\sqrt 5 - 1} \right)\\ E = 2.\left( {5 - 1} \right) = 8 \end{array}$
