LHS $ = \sqrt {25 + 3 + 2 \times 5 \times \sqrt 3 } - \sqrt {3 + 1 + 2 \times \sqrt 3 \times 1} $
$ = \sqrt {{5^2} + {{\sqrt 3 }^2} + 2 \times 5 \times \sqrt 3 } - \sqrt {{{\sqrt 3 }^2} + {1^2} + 2 \times \sqrt 3 \times 1} $
$ = \sqrt {{{(5 + \sqrt 3 )}^2}} - \sqrt {{{(\sqrt 3 + 1)}^2}} $
$ = (5 + \sqrt 3 ) - (\sqrt 3 + 1) = 4$
RHS $ = \sqrt 3 + \sqrt 2 \approx 3.14 \approx \pi$
Clearly, $4 > 3.14$
