Question

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

Accepted Answer

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

Comparison of radical values

Explanation

Practise this under exam conditions