№ 1. Сократите дробь

1. $$\frac{\sqrt{y^2+2y}}{\sqrt{y}} = \frac{\sqrt{y(y+2)}}{\sqrt{y}} = \sqrt{\frac{y(y+2)}{y}} = \sqrt{y+2}$$
2. $$\frac{\sqrt[3]{a^3-a^2}}{\sqrt{a}} = \frac{\sqrt[3]{a^2(a-1)}}{\sqrt{a}} = \frac{\sqrt[3]{a^2} \cdot \sqrt[3]{a-1}}{\sqrt{a}} = a^{\frac{2}{3}} \cdot (a-1)^{\frac{1}{3}} \cdot a^{-\frac{1}{2}} = a^{\frac{2}{3}-\frac{1}{2}} \cdot (a-1)^{\frac{1}{3}} = a^{\frac{4-3}{6}} \cdot (a-1)^{\frac{1}{3}} = a^{\frac{1}{6}} \cdot (a-1)^{\frac{1}{3}} = \sqrt[6]{a} \cdot \sqrt[3]{a-1}$$
3. $$\frac{\sqrt{6x^2-3x}}{\sqrt{x}} = \frac{\sqrt{3x(2x-1)}}{\sqrt{x}} = \sqrt{\frac{3x(2x-1)}{x}} = \sqrt{3(2x-1)} = \sqrt{6x-3}$$