Решение:

1. a) $$ 6\sqrt{3} = \sqrt{6^2 \cdot 3} = \sqrt{36 \cdot 3} = \sqrt{108} $$
2. б) $$ -6\sqrt{5} = -\sqrt{6^2 \cdot 5} = -\sqrt{36 \cdot 5} = -\sqrt{180} $$
3. в) $$ 5y\sqrt{y} = \sqrt{(5y)^2 \cdot y} = \sqrt{25y^2 \cdot y} = \sqrt{25y^3} $$
4. г) $$ 10b^3\sqrt{\frac{b}{2}} = \sqrt{(10b^3)^2 \cdot \frac{b}{2}} = \sqrt{100b^6 \cdot \frac{b}{2}} = \sqrt{50b^7} $$

Ответ:

1. a) $$\sqrt{108}$$
2. б) $$- \sqrt{180}$$
3. в) $$\sqrt{25y^3}$$
4. г) $$\sqrt{50b^7}$$