1. Упростите выражения: а) \(\frac{1}{5}\sqrt{300} - 4\sqrt{\frac{3}{16}} - \sqrt{75}\) б) \((3\sqrt{2}-1)(\sqrt{8}+2)\) в) \((\sqrt{5}+2)^2 - (3-\sqrt{5})^2\)

1. Упростите выражения:

1. а)

   \(\frac{1}{5}\sqrt{300} - 4\sqrt{\frac{3}{16}} - \sqrt{75}\) = \(\frac{1}{5} \cdot 10\sqrt{3} - 4 \cdot \frac{\sqrt{3}}{4} - 5\sqrt{3}\) = \(2\sqrt{3} - \sqrt{3} - 5\sqrt{3}\) = \(-4\sqrt{3}\)

2. б)

   \((3\sqrt{2}-1)(\sqrt{8}+2)\) = \((3\sqrt{2}-1)(2\sqrt{2}+2)\) = \(3\sqrt{2} \cdot 2\sqrt{2} + 3\sqrt{2} \cdot 2 - 1 \cdot 2\sqrt{2} - 1 \cdot 2\) = \(12 + 6\sqrt{2} - 2\sqrt{2} - 2\) = \(10 + 4\sqrt{2}\)

3. в)

   \((\sqrt{5}+2)^2 - (3-\sqrt{5})^2\) = \((5 + 4\sqrt{5} + 4) - (9 - 6\sqrt{5} + 5)\) = \((9 + 4\sqrt{5}) - (14 - 6\sqrt{5})\) = \(9 + 4\sqrt{5} - 14 + 6\sqrt{5}\) = \(-5 + 10\sqrt{5}\)

Ответ: а) -4√3; б) 10 + 4√2; в) -5 + 10√5.