Quantitative Aptitude Ques 1422

Question: The greatest among the numbers $ \sqrt[4]{2}, $ $ \sqrt[5]{3}, $ $ \sqrt[10]{6}, $ $ \sqrt[20]{15} $ is

Options:

A) $ \sqrt[20]{15} $

B) $ \sqrt[4]{2} $

C) $ \sqrt[5]{3} $

D) $ \sqrt[10]{6} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • In $ \sqrt[x]{a}, $ $ a $ is called base and x is called the radical. Now, first take the LCM of 4, 5, 10 and 20. LCM of 4, 5, 10 and $ 20=20 $ $ \sqrt[4]{2}={{(2)}^{\frac{1}{4}}}={{(2^{5})}^{\frac{1}{20}}}={{(32)}^{\frac{1}{20}}} $ $ [\because \sqrt[x]{y}={y^{1/x}}] $ $ \sqrt[5]{3}={{(3)}^{\frac{1}{5}}}={{(3^{4})}^{\frac{1}{20}}}={{(81)}^{\frac{1}{20}}} $ $ \sqrt[10]{6}={{(6)}^{\frac{1}{10}}}={{(6^{2})}^{\frac{1}{20}}}={{(36)}^{\frac{1}{20}}} $ $ \sqrt[20]{15}={{(15)}^{\frac{1}{20}}} $ Thus, greatest number is $ {{(81)}^{\frac{1}{20}}}, $ i.e. $ \sqrt[5]{3}. $
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