Упростите выражение: a) $$\frac{4}{5} \sqrt{75} + \sqrt{2}(\sqrt{8} - \sqrt{24})$$; б) $$(\sqrt{8} - \sqrt{5})^2$$.

a) $$\frac{4}{5} \sqrt{75} + \sqrt{2}(\sqrt{8} - \sqrt{24}) = \frac{4}{5} \sqrt{25 \cdot 3} + \sqrt{2}(\sqrt{4 \cdot 2} - \sqrt{4 \cdot 6}) = \frac{4}{5} \cdot 5 \sqrt{3} + \sqrt{2}(2\sqrt{2} - 2\sqrt{6}) = 4\sqrt{3} + 2\sqrt{2}\sqrt{2} - 2\sqrt{2}\sqrt{6} = 4\sqrt{3} + 2 \cdot 2 - 2\sqrt{12} = 4\sqrt{3} + 4 - 2\sqrt{4 \cdot 3} = 4\sqrt{3} + 4 - 2 \cdot 2 \sqrt{3} = 4\sqrt{3} + 4 - 4\sqrt{3} = 4$$.

б) $$(\sqrt{8} - \sqrt{5})^2 = (\sqrt{8})^2 - 2\sqrt{8}\sqrt{5} + (\sqrt{5})^2 = 8 - 2\sqrt{40} + 5 = 13 - 2\sqrt{4 \cdot 10} = 13 - 2 \cdot 2 \sqrt{10} = 13 - 4\sqrt{10}$$.

Ответ:

a) 4, б) $$13 - 4\sqrt{10}$$.