Решение:

1. а) $$4\sqrt{2} = \sqrt{4^2} \cdot \sqrt{2} = \sqrt{16 \cdot 2} = \sqrt{32}$$
2. б) $$-3\sqrt{5} = -\sqrt{3^2} \cdot \sqrt{5} = -\sqrt{9 \cdot 5} = -\sqrt{45}$$
3. в) $$\frac{2}{3}\sqrt{63} = \sqrt{(\frac{2}{3})^2} \cdot \sqrt{63} = \sqrt{\frac{4}{9} \cdot 63} = \sqrt{\frac{4 \cdot 63}{9}} = \sqrt{\frac{4 \cdot 7 \cdot 9}{9}} = \sqrt{4 \cdot 7} = \sqrt{28}$$
4. г) $$\frac{-1}{2}\sqrt{8} = -\sqrt{(\frac{1}{2})^2} \cdot \sqrt{8} = -\sqrt{\frac{1}{4} \cdot 8} = -\sqrt{\frac{8}{4}} = -\sqrt{2}$$
5. д) $$4\sqrt{2,5} = \sqrt{4^2} \cdot \sqrt{2,5} = \sqrt{16 \cdot 2,5} = \sqrt{40}$$