Президентский ФМЛ №239

Эта страница только для чтения. Вы можете посмотреть её исходный текст, но не можете его изменить. Сообщите администратору, если считаете, что это неправильно.
^  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.   |  \\ $\sqrt{\dfrac{\sqrt{7}+\sqrt{5}+\sqrt{3}}{2}\cdot\dfrac{\sqrt{7}-\sqrt{5}+\sqrt{3}}{2}\cdot\dfrac{\sqrt{7}+\sqrt{5}-\sqrt{3}}{2}\cdot\dfrac{\sqrt{3}+\sqrt{5}-\sqrt{7}}{2}}$\\                                                                                                                                                  |  \\  $\dfrac{\sqrt{59}}{4}$                                           |