1. Упростите выражение: a) $$\frac{2}{3}\sqrt{27} + \sqrt{2(\sqrt{8} - \sqrt{6})}$$; б) $$(\sqrt{7} - \sqrt{3})^2$$.

a) $$\frac{2}{3}\sqrt{27} + \sqrt{2(\sqrt{8} - \sqrt{6})}$$ $$\frac{2}{3}\sqrt{27} = \frac{2}{3}\sqrt{9 \cdot 3} = \frac{2}{3} \cdot 3\sqrt{3} = 2\sqrt{3}$$ $$\sqrt{2(\sqrt{8} - \sqrt{6})} = \sqrt{2(2\sqrt{2} - \sqrt{6})} = \sqrt{4\sqrt{2} - 2\sqrt{6}} = \sqrt{4\sqrt{2} - 2\sqrt{2}\sqrt{3}} = \sqrt{2\sqrt{2}(2 - \sqrt{3})}$$ Итого: $$2\sqrt{3} + \sqrt{4\sqrt{2} - 2\sqrt{6}}$$ б) $$(\sqrt{7} - \sqrt{3})^2 = (\sqrt{7})^2 - 2(\sqrt{7})(\sqrt{3}) + (\sqrt{3})^2 = 7 - 2\sqrt{21} + 3 = 10 - 2\sqrt{21}$$ Ответ: a) $$2\sqrt{3} + \sqrt{4\sqrt{2} - 2\sqrt{6}}$$ б) $$\boxed{10 - 2\sqrt{21}}$$