10. 1/2 √200 - 7 √2/49 - √72 =

$$\frac{1}{2} \sqrt{200} - 7\sqrt{\frac{2}{49}} - \sqrt{72} = \frac{1}{2} \sqrt{100 \cdot 2} - 7 \frac{\sqrt{2}}{7} - \sqrt{36 \cdot 2} = \frac{1}{2} \cdot 10\sqrt{2} - \sqrt{2} - 6\sqrt{2} = 5\sqrt{2} - \sqrt{2} - 6\sqrt{2} = (5 - 1 - 6)\sqrt{2} = -2\sqrt{2}$$