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1). \(\sqrt 5 \)2). \(\sqrt[3]{6}\)3). \(\sqrt[4]{7}\)4). \(\sqrt[6]{8}\) |
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Answer» $(\sqrt 5= {5^{\frac{1}{2}}},\;\sqrt[3]{6} = {6^{\frac{1}{3}}},\;\sqrt[4]{7} = {7^{\frac{1}{4}}},\;\sqrt[6]{8} = {8^{\frac{1}{6}}})$ LCM of denominators of exponents = LCM (2, 3, 4, 6) = 12 $({5^{\frac{1}{2} \times \frac{{12}}{{12}}}},\;{6^{\frac{1}{3} \times \frac{{12}}{{12}}}},\;{7^{\frac{1}{4} \times \frac{{12}}{{12}}}},\;{8^{\frac{1}{6} \times \frac{{12}}{{12}}}} = {5^{\frac{6}{{12}}}},\;{6^{\frac{4}{{12}}}},\;{7^{\frac{3}{{12}}}},\;{8^{\frac{2}{{12}}}})$ 56 > 64 > 73 > 82 ∴ √5 is the greatest |
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