I have an elementary question I hope I could be helped with: is $$\sqrt{x^2+9}$$ where $x$ is an integer, rational only for $x=0$?

@Sahaj The only other solutions are $x=-4$ and $x=4$.

Thanks a lot @Peter

How do you show that those are the only ones?

Oh wait I think I can do this one.

@Peter Could you use your softwares for also checking $$\sqrt{x^5+9}$$ and whether it is ever rational over integer $x$ other than $0$?

Sorry for the multiple pings, editing doesn't work well on mobile