1. Найдите значение корня: 1) a) √49/64; б) √81/100; в) √9/25; г) √36/121; 2) a) √3 6/25; б) √2 46/49; в) √11 1/9; г) √3 13/36.

Решение:

1) a) \[\sqrt{\frac{49}{64}} = \frac{\sqrt{49}}{\sqrt{64}} = \frac{7}{8}\] б) \[\sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}} = \frac{9}{10}\] в) \[\sqrt{\frac{9}{25}} = \frac{\sqrt{9}}{\sqrt{25}} = \frac{3}{5}\] г) \[\sqrt{\frac{36}{121}} = \frac{\sqrt{36}}{\sqrt{121}} = \frac{6}{11}\] 2) a) \[\sqrt{3 \frac{6}{25}} = \sqrt{\frac{3 \cdot 25 + 6}{25}} = \sqrt{\frac{75 + 6}{25}} = \sqrt{\frac{81}{25}} = \frac{\sqrt{81}}{\sqrt{25}} = \frac{9}{5} = 1\frac{4}{5}\] б) \[\sqrt{2 \frac{46}{49}} = \sqrt{\frac{2 \cdot 49 + 46}{49}} = \sqrt{\frac{98 + 46}{49}} = \sqrt{\frac{144}{49}} = \frac{\sqrt{144}}{\sqrt{49}} = \frac{12}{7} = 1\frac{5}{7}\] в) \[\sqrt{11 \frac{1}{9}} = \sqrt{\frac{11 \cdot 9 + 1}{9}} = \sqrt{\frac{99 + 1}{9}} = \sqrt{\frac{100}{9}} = \frac{\sqrt{100}}{\sqrt{9}} = \frac{10}{3} = 3\frac{1}{3}\] г) \[\sqrt{3 \frac{13}{36}} = \sqrt{\frac{3 \cdot 36 + 13}{36}} = \sqrt{\frac{108 + 13}{36}} = \sqrt{\frac{121}{36}} = \frac{\sqrt{121}}{\sqrt{36}} = \frac{11}{6} = 1\frac{5}{6}\]