$\begin{array}{l}a)\,2\sqrt{3}(\sqrt{27} + 2\sqrt{48} - \sqrt{75})^2\\ =2\sqrt{3}(\sqrt{9.3} + 2\sqrt{16.3} - \sqrt{25.3})^2\\ = 2\sqrt{3}(3\sqrt{3} + 8\sqrt{3} - 5\sqrt{3})^2\\ = 2\sqrt{3}(6\sqrt{3})^2\\ = 2\sqrt{3}.36.3\\ =216\sqrt{3}\\\\ b)\, (2\sqrt{2} - \sqrt{3})^2\\ = (2\sqrt{2})^2 - 2.2\sqrt{2}.\sqrt{3} + (\sqrt{3})^2\\ = 8 - 4\sqrt{6} + 3\\ = 11 - 4\sqrt{6}\\\\ c)\,(\sqrt{3 - \sqrt{5}} + \sqrt{3 + \sqrt{5}})^2\\ = (\sqrt{3 - \sqrt{5}})^2 + 2\sqrt{(3 - \sqrt{5})(3 + \sqrt{5})} + (\sqrt{3 + \sqrt{5}})^2\\ = 3 - \sqrt{5} + 2\sqrt{3^2 - \sqrt{5^2}} + 3 + \sqrt{5}\\ = 6 - 2\sqrt{4}\\ = 6 - 2.2 = 2\\\\ d)\, (\sqrt{6} + \sqrt{2})(\sqrt{3} - 2)\sqrt{\sqrt{3} +2}\\ = \sqrt{2}(\sqrt{3} + 1)(\sqrt{3} - 2)\sqrt{\sqrt{3} +2}\\ = (\sqrt{3} + 1)(\sqrt{3} - 2)\sqrt{2\sqrt{3} +4}\\ = (\sqrt{3} + 1)(\sqrt{3} - 2)\sqrt{\sqrt{3^2} + 2\sqrt{3} +1}\\ = (\sqrt{3} + 1)(\sqrt{3} - 2)\sqrt{(\sqrt{3} +1)^2}\\ = (\sqrt{3} + 1)(\sqrt{3} - 2)(\sqrt{3} + 1)\\ = (\sqrt{3} + 1)^2(\sqrt{3} - 2)\\ = (\sqrt{3^2} + 2\sqrt{3} +1)(\sqrt{3} - 2)\\ = (4 + 2\sqrt{3})(\sqrt{3} - 2)\\ = 4\sqrt{3} - 8 + 2\sqrt{3}.\sqrt{3} - 4\sqrt{3}\\ = -8 + 2.3\\ = - 8 + 6 = -2 \end{array}$
