math-public:uproscheniya_s_chislami
| Номер | ————————— Условие ————————— | ——————— Ответ ——————— |
|---|---|---|
| 1. | $\dfrac{3\sqrt{10}}{2}\cdot\left(\dfrac{\sqrt{7}}{2+\sqrt{5}}+\dfrac{\sqrt{5}}{2-\sqrt{7}}+\dfrac{4}{\sqrt{7}+\sqrt{5}}\right)-5\sqrt{14}$ | $-20\sqrt{2}$ |
| 2. | $2(3-\sqrt{5})(\sqrt{3}-5)+\dfrac{2}{\sqrt{3}-\sqrt{5}}+(\sqrt{15}+1)^2-\sqrt{405}$ | $5 \sqrt{3}-14$ |
| 3. | $\left(\dfrac{\sqrt{21}-7}{3-\sqrt{21}}-\dfrac{\sqrt{15}-5}{3\sqrt{2}-\sqrt{30}}\right)\cdot\dfrac{\sqrt{3}}{\sqrt{14}-\sqrt{5}}$ | $\dfrac{\sqrt{2}}{2}$ |
| 4. | $\left(\dfrac{1}{\sqrt{8}+1}-\dfrac{1}{\sqrt{2}+1}+\sqrt{2\dfrac{30}{49}}\right)(2-\sqrt{2})$ | $\dfrac{6}{7}$ |
| 5. | $\left(\dfrac{2}{\sqrt{\sqrt{3}+1}-2}-\dfrac{2}{\sqrt{\sqrt{3}+1}+2}\right)(\sqrt{27}-9)$ | $24$ |
| 6. | $\left(\dfrac{\sqrt{14}-\sqrt{21}}{\sqrt{7}-7}:\left(\sqrt{\dfrac{2}{3}}-1\right)+\sqrt{\dfrac{21}{36}}\right)\cdot(6-\sqrt{243})-4,\!5$ | $-\sqrt{3}$ |
| 7. | $\left(\dfrac{(2-\sqrt{5})(3+\sqrt{15})}{\sqrt{3}-\sqrt{5}}-4\sqrt{15}\right)\cdot\left(\sqrt{\dfrac{3}{5}}+\sqrt{\dfrac{5}{3}}-2\right)-(\sqrt{3}+\sqrt{15})^{2}+\dfrac{34}{\sqrt{5}}$ | $8\sqrt{15}-48$ |
| 8. | $\left(\sqrt{\dfrac{45}{2}}-\dfrac{3}{\sqrt{5}}\right)(\sqrt{50}+2)+\dfrac{7-\sqrt{5}}{7+\sqrt{5}}\cdot44+\dfrac{2\sqrt{5}}{3}-54$ | $\dfrac{7\sqrt{5}}{15}$ |
| 9. | $\left(\dfrac{8+\sqrt{8}}{1+\dfrac{1}{\sqrt{8}}}-\sqrt{2}\right)\cdot\dfrac{\dfrac{1}{\sqrt{2}}+\sqrt{2}-1}{\dfrac{1}{\sqrt{2}}-\sqrt{2}+1}-15\sqrt{2}$ | $4$ |
| 10. | $\dfrac{\dfrac{3-2\sqrt{2}}{2\sqrt{2}+3}-\dfrac{2+\sqrt{3}}{\sqrt{3}-2}+\sqrt{288}}{\dfrac{6+\sqrt{2}}{\sqrt{2}-\sqrt{3}}-\sqrt{7-4\sqrt{3}}-\sqrt{3}+1}$ | $4(\sqrt{2}-\sqrt{3})$ |
| 11. | $\dfrac{\sqrt{7-\sqrt{24}}-\sqrt{7-\sqrt{48}}}{\sqrt{5-\sqrt{24}}}-\dfrac{3}{\sqrt{3}-\sqrt{6}}$ | $3+2\sqrt{6}$ |
| 12. | $\dfrac{\left(\dfrac{2}{\sqrt{3}}-\dfrac{\sqrt{2}}{3}+1\right)(2\sqrt{3}+\sqrt{2}+3)-\dfrac{1}{3}}{\dfrac{\sqrt{24}-\sqrt{72}}{\sqrt{2}-\sqrt{6}}+2}\cdot(3-\sqrt{3})$ | $3$ |
| 13. | $\dfrac{\dfrac{3\sqrt{3}+2\sqrt{2}}{5-\sqrt{6}}-\dfrac{\sqrt{5}+\sqrt(4+\dfrac{4}{5})}{(\sqrt{2}+\sqrt{3})^2}}{1+\sqrt{1,\!5}-\dfrac{\sqrt{2,\!5}}{5}}$ | $\sqrt{2}$ |
| 14. | $\dfrac{\sqrt{28+6\sqrt{3}}+1}{\sqrt{4+2\sqrt{3}}-1}\cdot\dfrac{9-2\sqrt{3}}{\sqrt{12+6\sqrt{3}}-3}$ | $\dfrac{23}{\sqrt{3}}$ |
| 15. | $\dfrac{(4-\sqrt{15})\sqrt(4+\sqrt{15})-(4+\sqrt{15})\sqrt(4-\sqrt{15})}{\left(\sqrt{\dfrac{6}{11}}-\sqrt{2}\right)(\sqrt{1,\!5}+\sqrt{5,\!5})}$ | $\dfrac{\sqrt{66}}{8}$ |
| 16. | $\sqrt{-5+8\sqrt{12\sqrt{3}+6\sqrt{7-4\sqrt{3}}}}\cdot(4-\sqrt{3})$ | $13$ |
| 17. | $\dfrac{\sqrt{98}+\sqrt{250}-4\sqrt{\dfrac{5}{2}}+\sqrt{160}}{5\sqrt{\dfrac{2}{5}}+8\sqrt{\dfrac{5}{8}}+\sqrt{160}-7\sqrt{2}}+\left(\dfrac{1-\sqrt{5}}{\sqrt{5}-2}\right)^2-\dfrac{13\sqrt{5}}{2}$ | $\dfrac{31}{2}$ |
| 18. | $\dfrac{1}{\sqrt{8-2\sqrt{7}}+2\sqrt{7}}+\dfrac{\sqrt{7}+7}{21+\sqrt{7}}-\dfrac{\sqrt{175}}{62}$ | $\dfrac{21}{62}$ |
| 19. | $\dfrac{(\sqrt{3}-2)^4+56\sqrt{3}-96}{(1+\sqrt{5})^2-(2-\sqrt{5})^2}\cdot\dfrac{76}{\sqrt{21+4\sqrt{5}}}$ | $\dfrac{4}{3}$ |
| 20. | $\dfrac{(5\sqrt{112}+2\sqrt{567}-9\sqrt{175}):(2\sqrt{7})}{\left(7\sqrt{\dfrac{8}{7}}-14\sqrt{\dfrac{3}{7}}+3\sqrt{\dfrac{7}{2}}\right)\cdot2\sqrt{\dfrac{2}{7}}-14}$ | $\dfrac{7\sqrt{6}}{48}$ |
| 21. | $\dfrac{\dfrac{4}{\sqrt{2}+\sqrt{3}-1}-\sqrt{10-4\sqrt{6}}}{(1+\sqrt{3,\!75})^2-\sqrt{15}}$ | $\dfrac{4\sqrt{2}}{19}$ |
| 22. | $\dfrac{(3\sqrt{245}-\sqrt{810}):(2\sqrt{5})+4,\!5\sqrt{2}}{\left(2\sqrt{0,\!3}+3\sqrt{1\dfrac{2}{3}}\right)\cdot4\sqrt{\dfrac{5}{3}}-20}-\dfrac{10,\!5}{2\sqrt{6}-2\sqrt{2}}$ | $-\dfrac{21\sqrt{6}}{16}$ |
| 23. | $\dfrac{(\sqrt{2}-\sqrt{3})^3+(\sqrt{2}+\sqrt{3})^3}{\dfrac{14}{4-\sqrt{2}}+(\sqrt{2}-1)^2-7}$ | $-22$ |
| 24. | $\dfrac{\sqrt{(3-\sqrt{7})^2+5}\cdot\sqrt{21+\sqrt{252}}-\dfrac{\sqrt{73,\!5}}{\sqrt{3,\!5}}}{\left(3\sqrt{\dfrac{32}{3}}-\sqrt{\dfrac{3}{8}}\right)\cdot\sqrt{\dfrac{3}{2}}-12}$ | $-\dfrac{8 \sqrt{21}}{3}$ |
| 25. | $\dfrac{(2-\sqrt{6})(\sqrt{2}-\sqrt{6})+2\sqrt{3}+2\sqrt{6}}{\sqrt{11+6\sqrt{2}}}-\dfrac{2\sqrt{5}+\sqrt{30}}{\sqrt{30}-2\sqrt{5}}+\sqrt{24}$ | $-3$ |
| 26. | $\dfrac{(\sqrt{2}+\sqrt{3}-\sqrt{5})\cdot\sqrt{30}+5\sqrt{6}}{(\sqrt{90}+\sqrt{240}):(2\sqrt{3})-\sqrt{5}}\cdot\sqrt{10}+\dfrac{\sqrt{11-2\sqrt{30}}}{\sqrt{5}+\sqrt{6}}$ | $11$ |
| 27. | $\dfrac{\dfrac{1+\sqrt{3}}{3-\sqrt{3}}-\dfrac{3-\sqrt{3}}{1+\sqrt{3}}-4}{\dfrac{1-\sqrt{2}}{2+\sqrt{2}}+\dfrac{1+\sqrt{2}}{2-\sqrt{2}}+1}+\sqrt{-13+4\sqrt{28-10\sqrt{3}}}-2$ | $-\dfrac{19 \sqrt{3}}{15}$ |
| 28. | $\sqrt{\dfrac{5\sqrt{3}-3\sqrt{5}}{5\sqrt{3}+3\sqrt{5}}}-\sqrt{\dfrac{5\sqrt{3}+3\sqrt{5}}{5\sqrt{3}-3\sqrt{5}}}+2\sqrt{6}$ | $\sqrt{6}$ |
| 29. | $\dfrac{(\sqrt{4-\sqrt{2}}-\sqrt{4+\sqrt{2}})^2+2\sqrt{14}}{\sqrt{21-12\sqrt{3}}-\sqrt{39+12\sqrt{3}}}+\dfrac{4}{13\sqrt{3}}$ | $-\dfrac{12}{13}$ |
| 30. | $\sqrt{\dfrac{\sqrt{7}+\sqrt{5}+\sqrt{3}}{2}\cdot\dfrac{\sqrt{7}-\sqrt{5}+\sqrt{3}}{2}\cdot\dfrac{\sqrt{7}+\sqrt{5}-\sqrt{3}}{2}\cdot\dfrac{\sqrt{3}+\sqrt{5}-\sqrt{7}}{2}}$ | $\dfrac{\sqrt{59}}{4}$ |
math-public/uproscheniya_s_chislami.txt · Последнее изменение: 2016/10/26 13:22 — labreslav