Ordering Surds and Radicals

Take LCM of orders of radicals $4, 3, 6, 6$, which is $12$.

A) $\sqrt[4]{3} = 3^{1/4} = 3^{3/12} = (3^3)^{1/12} = 27^{1/12}$ B) $\sqrt[3]{2} = 2^{1/3} = 2^{4/12} = (2^4)^{1/12} = 16^{1/12}$ C) $\sqrt[6]{5} = 5^{1/6} = 5^{2/12} = (5^2)^{1/12} = 25^{1/12}$ D) $\sqrt[6]{7} = 7^{1/6} = 7^{2/12} = (7^2)^{1/12} = 49^{1/12}$

Comparing $16 < 25 < 27 < 49 \implies B < C < A < D$.

Hence, Option B is correct.