abstract algebra - Linear independence of $n$th roots over $mathbb{Q}$

I know that the set of square roots of distinct square-free integers is linearly independent over $\mathbb{Q}$. To generalize this fact, define

$R_n = \{ \sqrt[n]{s} \mid s\text{ integer with prime factorization }s = p_1^{a_1} \ldots p_k^{a_k}, \text{ where } 0 \leq a_i < n \}$

For example, $R_2$ is the set of square roots of square-free integers.

Question: Is $R_n$ linearly independent over $\mathbb{Q}$ for all $n \geq 2$?

Harder (?) question: Is $\cup_{n\geq2}R_n$ linearly independent over $\mathbb{Q}$?