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Arrange them in ascending order \(\sqrt[4]{6},\sqrt[3]{3}\) and \(\sqrt[3]{4}\)1). \(\sqrt[3]{3} < \sqrt[4]{6} > \sqrt[3]{4}\)2). \(\sqrt[3]{3} > \sqrt[4]{6} > \sqrt[3]{4}\)3).4). \(\sqrt[3]{3} < \sqrt[4]{6} < \sqrt[3]{4}\) |
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Answer» $(\Rightarrow \sqrt[4]{6} = {6^{\frac{1}{{4}}}} = {6^{\frac{3}{{12}}}} = \left( {216} \right){^{\frac{1}{{12}}}})$ $(\Rightarrow \sqrt[3]{3} = {3^{\frac{1}{3}}} = {3^{\frac{4}{{12}}}} = {\left( {81} \right)^{\frac{1}{{12}}}})$ $(\begin{array}{l} \Rightarrow \sqrt[3]{4} = {4^{\frac{1}{3}}} = {4^{\frac{4}{{12}}}} = {\left( {256} \right)^{\frac{1}{{12}}}}\\ \therefore \sqrt[3]{3} < \sqrt[4]{6} < \sqrt[3]{4} \end{array})$ |
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