Comparison of radical values

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Surds and Indices

If $x = \sqrt[5]{6}$ and $y = \sqrt[4]{5}$ , Which of the following is true?

Answer

LCM of the orders of roots (5 and 4) is 20. $x = 6^{1/5} = (6^4)^{1/20} = (1296)^{1/20}$ $y = 5^{1/4} = (5^5)^{1/20} = (3125)^{1/20}$

Since $3125 > 1296$ , $y > x$ .

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