Вычислите:

1. а) $$\sqrt{113^2 - 112^2} = \sqrt{(113-112)(113+112)} = \sqrt{1 \cdot 225} = \sqrt{225} = 15$$
2. б) $$\sqrt{50^2 - 14^2} = \sqrt{(50-14)(50+14)} = \sqrt{36 \cdot 64} = \sqrt{36} \cdot \sqrt{64} = 6 \cdot 8 = 48$$
3. в) $$\sqrt{176^2 - 112^2} = \sqrt{(176-112)(176+112)} = \sqrt{64 \cdot 288} = \sqrt{64} \cdot \sqrt{288} = 8 \cdot \sqrt{144 \cdot 2} = 8 \cdot 12 \cdot \sqrt{2} = 96\sqrt{2} $$
4. г) $$\sqrt{\frac{145.5^2-96.5^2}{193.5^2-31.5^2}} = \sqrt{\frac{(145.5-96.5)(145.5+96.5)}{(193.5-31.5)(193.5+31.5)}} = \sqrt{\frac{49 \cdot 242}{162 \cdot 225}} = \sqrt{\frac{49 \cdot 2 \cdot 121}{2 \cdot 81 \cdot 225}} = \sqrt{\frac{49 \cdot 121}{81 \cdot 225}} = \frac{\sqrt{49} \cdot \sqrt{121}}{\sqrt{81} \cdot \sqrt{225}} = \frac{7 \cdot 11}{9 \cdot 15}} = \frac{77}{135}$$