Question 1117328
To ease the notation,  let  A = {{{ sqrt(3 + sqrt(5)) }}}   and B = {{{ sqrt(3 - sqrt(5)) }}}

Then the Left Hand Side is  {{{ (A - B) ^2 }}}

{{{ (A-B)^2  = A^2 - 2AB + B^2  = (A^2+B^2) - 2AB }}}

{{{ A^2 =  3 + sqrt(5) }}}
{{{ B^2 = 3 - sqrt(5) }}}

{{{ A^2 + B^2  =  6 }}}

{{{ -2AB = -2(sqrt(3+sqrt(5))) * (sqrt(3-sqrt(5)))  = -2(sqrt(9-5)) = -2(2) = -4 }}}

so  {{{ (A^2+B^2) -2AB = 6-4 = 2 }}}  Done.