1137. a) √3, ⁴√4 и ⁸√7; б) √2, ³√3 и ⁴√4; в) √6, ⁴√17 и ⁸√40; г) ⁵√3, √2 и ¹⁵√100.

1137. a) \( \sqrt{3}, \sqrt[4]{4}, \sqrt[8]{7} \). Показатели: 2, 4, 8. НОЗ(2, 4, 8) = 8. \( \sqrt{3} = 3^{\frac{1}{2}} = 3^{\frac{4}{8}} = \sqrt[8]{3^4} = \sqrt[8]{81} \) \( \sqrt[4]{4} = 4^{\frac{1}{4}} = 4^{\frac{2}{8}} = \sqrt[8]{4^2} = \sqrt[8]{16} \) \( \sqrt[8]{7} \) б) \( \sqrt{2}, \sqrt[3]{3}, \sqrt[4]{4} \). Показатели: 2, 3, 4. НОЗ(2, 3, 4) = 12. \( \sqrt{2} = 2^{\frac{1}{2}} = 2^{\frac{6}{12}} = \sqrt[12]{2^6} = \sqrt[12]{64} \) \( \sqrt[3]{3} = 3^{\frac{1}{3}} = 3^{\frac{4}{12}} = \sqrt[12]{3^4} = \sqrt[12]{81} \) \( \sqrt[4]{4} = 4^{\frac{1}{4}} = 4^{\frac{3}{12}} = \sqrt[12]{4^3} = \sqrt[12]{64} \) в) \( \sqrt{6}, \sqrt[4]{17}, \sqrt[8]{40} \). Показатели: 2, 4, 8. НОЗ(2, 4, 8) = 8. \( \sqrt{6} = 6^{\frac{1}{2}} = 6^{\frac{4}{8}} = \sqrt[8]{6^4} = \sqrt[8]{1296} \) \( \sqrt[4]{17} = 17^{\frac{1}{4}} = 17^{\frac{2}{8}} = \sqrt[8]{17^2} = \sqrt[8]{289} \) \( \sqrt[8]{40} \) г) \( \sqrt[5]{3}, \sqrt{2}, \sqrt[15]{100} \). Показатели: 5, 2, 15. НОЗ(5, 2, 15) = 30. \( \sqrt[5]{3} = 3^{\frac{1}{5}} = 3^{\frac{6}{30}} = \sqrt[30]{3^6} = \sqrt[30]{729} \) \( \sqrt{2} = 2^{\frac{1}{2}} = 2^{\frac{15}{30}} = \sqrt[30]{2^{15}} = \sqrt[30]{32768} \) \( \sqrt[15]{100} = 100^{\frac{1}{15}} = (10^2)^{\frac{1}{15}} = 10^{\frac{2}{15}} = 10^{\frac{4}{30}} = \sqrt[30]{10^4} = \sqrt[30]{10000} \)