Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 39

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\[1)\ \sqrt[3]{\frac{64}{125}} = \frac{\sqrt[3]{64}}{\sqrt[3]{125}} = \frac{\sqrt[3]{4^{3}}}{\sqrt[3]{5^{3}}} =\]

\[= \frac{4}{5} = 0,8\]

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

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

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

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

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

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

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