Taking N-th root of inequalities

Question

I'd like to know what are the rules for taking the N-th root in inequalities.

Suppose we have

$$ a < b $$

Is it always permitted to say that the following is correct?

$$ {\sqrt[n]a} < {\sqrt[n]b}$$

Thanks.

Answer 1

If $n$ is non negative, then I would say that it is even equivalent. If $n$ is negative, in particular $n=-2$ take the following counterexample: $2\leq3$ but $\frac{1}{\sqrt{2}}\geq\frac{1}{\sqrt{3}}$