Решение:

а) $$\begin{aligned} (\sqrt{6} - \sqrt{3})^2 + \sqrt{72} &= ((\sqrt{6})^2 - 2\sqrt{6}\sqrt{3} + (\sqrt{3})^2) + \sqrt{36 \cdot 2} \\ &= (6 - 2\sqrt{18} + 3) + 6\sqrt{2} \\ &= 9 - 2\sqrt{9 \cdot 2} + 6\sqrt{2} \\ &= 9 - 2 \cdot 3\sqrt{2} + 6\sqrt{2} \\ &= 9 - 6\sqrt{2} + 6\sqrt{2} \\ &= 9 \end{aligned}$$ Ответ: 9 б) $$\begin{aligned} (\sqrt{6} - \sqrt{3})(\sqrt{2} + \sqrt{6}) &= \sqrt{6}\sqrt{2} + \sqrt{6}\sqrt{6} - \sqrt{3}\sqrt{2} - \sqrt{3}\sqrt{6} \\ &= \sqrt{12} + 6 - \sqrt{6} - \sqrt{18} \\ &= \sqrt{4 \cdot 3} + 6 - \sqrt{6} - \sqrt{9 \cdot 2} \\ &= 2\sqrt{3} + 6 - \sqrt{6} - 3\sqrt{2} \end{aligned}$$ Ответ: $$2\sqrt{3} + 6 - \sqrt{6} - 3\sqrt{2}$$ в) $$\begin{aligned} (\sqrt{3} - \sqrt{8})(\sqrt{3} + 2\sqrt{2}) &= \sqrt{3}\sqrt{3} + 2\sqrt{2}\sqrt{3} - \sqrt{8}\sqrt{3} - 2\sqrt{8}\sqrt{2} \\ &= 3 + 2\sqrt{6} - \sqrt{24} - 2\sqrt{16} \\ &= 3 + 2\sqrt{6} - \sqrt{4 \cdot 6} - 2 \cdot 4 \\ &= 3 + 2\sqrt{6} - 2\sqrt{6} - 8 \\ &= -5 \end{aligned}$$ Ответ: -5