Решение:

1. a) $$\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}$$

2. б) $$\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}$$

3. в) $$\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}$$

4. г) $$\sqrt{\frac{20}{243}} = \sqrt{\frac{4 \times 5}{81 \times 3}} = \frac{\sqrt{4} \times \sqrt{5}}{\sqrt{81} \times \sqrt{3}} = \frac{2 \sqrt{5}}{9 \sqrt{3}} = \frac{2 \sqrt{5} \times \sqrt{3}}{9 \sqrt{3} \times \sqrt{3}} = \frac{2 \sqrt{15}}{27}$$

5. д) $$\sqrt{36b} = \sqrt{36} \times \sqrt{b} = 6\sqrt{b}$$

6. e) $$\sqrt{8a^6} = \sqrt{4 \times 2 \times a^6} = \sqrt{4 \times (a^3)^2 \times 2} = 2 \times a^3 \sqrt{2}=2a^3\sqrt{2}$$

Ответ:

• a) $$2\sqrt{7}$$
• б) $$5\sqrt{6}$$
• в) $$6\sqrt{3}$$
• г) $$\frac{2 \sqrt{15}}{27}$$
• д) $$6\sqrt{b}$$
• e) $$2a^3\sqrt{2}$$