a) $$5\sqrt{48} - 2\sqrt{75} = 5\sqrt{16 \cdot 3} - 2\sqrt{25 \cdot 3} = 5 \cdot 4\sqrt{3} - 2 \cdot 5\sqrt{3} = 20\sqrt{3} - 10\sqrt{3} = 10\sqrt{3}$$.
б) $$(3\sqrt{2} + \sqrt{18})\sqrt{2} = (3\sqrt{2} + \sqrt{9 \cdot 2})\sqrt{2} = (3\sqrt{2} + 3\sqrt{2})\sqrt{2} = 6\sqrt{2} \cdot \sqrt{2} = 6 \cdot 2 = 12$$.
в) $$(4 - \sqrt{5})^2 = 4^2 - 2 \cdot 4 \cdot \sqrt{5} + (\sqrt{5})^2 = 16 - 8\sqrt{5} + 5 = 21 - 8\sqrt{5}$$.
Ответ:
a) $$10\sqrt{3}$$; б) 12; в) $$21 - 8\sqrt{5}$$.