Prove or disprove:
If $a, b, c$ are sides of a triangle, then so are their $r^{th}$ roots $a^{1/r}, b^{1/r}, c^{1/r}$ where $r$ is a real number $\gt 1$.
If $a, b, c$ are sides of a triangle, then so are their $r^{th}$ roots $a^{1/r}, b^{1/r}, c^{1/r}$ where $r$ is a real number $\gt 1$.
