$\begin{array}{l} 1)\sqrt {27} - 2\sqrt 3 + 2\sqrt {48} - 3\sqrt {75} \\ = \sqrt {{3^2}.3} - 2\sqrt 3 + 2.\sqrt {{4^2}.3} - 3.\sqrt {{5^2}.3} \\ = 3\sqrt 3 - 2\sqrt 3 + 2.4\sqrt 3 - 3.5\sqrt 3 \\ = - 4\sqrt 3 \\ 2)\sqrt {{{\left( {\sqrt 5 - 2} \right)}^2}} - \dfrac{1}{2}\sqrt {20} \\ = \left| {\sqrt 5 - 2} \right| - \dfrac{1}{2}.\sqrt {{2^2}.5} = \sqrt 5 - 2 - \dfrac{1}{2}.2.\sqrt 5 \\ = \sqrt 5 - 2 - \sqrt 5 = - 2\\ 3)\left( {\dfrac{{\sqrt {10} - \sqrt 5 }}{{\sqrt 2 - 1}} + \dfrac{{\sqrt 6 + \sqrt 2 }}{{\sqrt 3 + 1}}} \right):\dfrac{1}{{\sqrt 5 - \sqrt 2 }}\\ = \left[ {\dfrac{{\sqrt 5 \left( {\sqrt 2 - 1} \right)}}{{\sqrt 2 - 1}} + \dfrac{{\sqrt 2 \left( {\sqrt 3 + 1} \right)}}{{\sqrt 3 + 1}}} \right].\left( {\sqrt 5 - \sqrt 2 } \right)\\ = \left( {\sqrt 5 + \sqrt 2 } \right)\left( {\sqrt 5 - \sqrt 2 } \right) = 5 - 2 = 3 \end{array}$
