Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 514

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\[1)\ \sqrt[4]{\frac{3}{4}} \bullet \sqrt[4]{6\frac{3}{4}} = \sqrt[4]{\frac{3}{4}} \bullet \sqrt[4]{\frac{6 \bullet 4 + 3}{4}} =\]

\[= \sqrt[4]{\frac{3}{4} \bullet \frac{27}{4}} = \sqrt[4]{\frac{3 \bullet 3^{3}}{2^{2} \bullet 2^{2}}} =\]

\[= \sqrt[4]{\frac{3^{4}}{2^{4}}} = \frac{3}{2} = 1,5;\]

\[2)\ \sqrt[3]{11\frac{1}{4}}\ :\sqrt[3]{3\frac{1}{3}} = \sqrt[3]{\frac{11 \bullet 4 + 1}{4}}\ :\]

\[:\sqrt[3]{\frac{3 \bullet 3 + 1}{3}} = \sqrt[3]{\frac{45}{4} \bullet \frac{3}{10}} =\]

\[= \sqrt[3]{\frac{9 \bullet 3}{4 \bullet 2}} = \sqrt[3]{\frac{3^{2} \bullet 3}{2^{2} \bullet 2}} =\]

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

\[3)\ \left( \sqrt{\sqrt[3]{16}} \right)^{3} = \left( \sqrt[{2 \bullet 3}]{16} \right)^{3} =\]

\[= \sqrt[{2 \bullet 3}]{16^{3}} = \sqrt{16} = \sqrt{4^{2}} = 4.\]