Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 447

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\[1)\ \sqrt[3]{\frac{64}{52}} = \sqrt[3]{\frac{16}{13}} = \sqrt[3]{\frac{2 \cdot 8}{13}} =\]

\[= 2\sqrt[3]{\frac{2}{13}};\]

\[2)\ \sqrt[4]{\frac{16}{81}} = \frac{\sqrt[4]{16}}{\sqrt[4]{81}} = \frac{\sqrt[4]{2^{4}}}{\sqrt[4]{3^{4}}} = \frac{2}{3};\]

\[3)\ \sqrt[3]{3\frac{3}{8}} = \sqrt[3]{\frac{3 \bullet 8 + 3}{8}} =\]

\[= \sqrt[3]{\frac{24 + 3}{8}} = \sqrt[3]{\frac{27}{8}} = \frac{\sqrt[3]{27}}{\sqrt[3]{8}} =\]

\[= \frac{\sqrt[3]{3^{3}}}{\sqrt[3]{2^{3}}} = \frac{3}{2} = 1,5.\]

\[4)\ \sqrt[5]{7\frac{19}{32}} = \sqrt[5]{\frac{7 \bullet 32 + 19}{32}} =\]

\[= \sqrt[5]{\frac{224 + 19}{32}} = \sqrt[5]{\frac{243}{32}} =\]

\[= \frac{\sqrt[5]{243}}{\sqrt[5]{32}} = \frac{\sqrt[5]{3^{5}}}{\sqrt[5]{2^{5}}} = \frac{3}{2} = 1,5.\]