Решение:

1. a) $$ \sqrt{162} = \sqrt{81 \cdot 2} = \sqrt{9^2 \cdot 2} = 9\sqrt{2} $$
2. б) $$ \sqrt{2\frac{1}{12}} = \sqrt{\frac{25}{12}} = \sqrt{\frac{25}{4 \cdot 3}} = \frac{5}{2\sqrt{3}} = \frac{5\sqrt{3}}{6} $$
3. в) $$ \sqrt{48y^3} = \sqrt{16 \cdot 3 \cdot y^2 \cdot y} = \sqrt{4^2 \cdot 3 \cdot y^2 \cdot y} = 4y\sqrt{3y} $$
4. г) $$ \sqrt{144a^5b^6} = \sqrt{12^2 \cdot a^4 \cdot a \cdot (b^3)^2} = 12a^2b^3\sqrt{a} $$

Ответ:

1. a) $$9\sqrt{2}$$
2. б) $$\frac{5\sqrt{3}}{6}$$
3. в) $$4y\sqrt{3y}$$
4. г) $$12a^2b^3\sqrt{a}$$