Root file system is full and I need to install additional software.

Solution 1:

To be honest, you're going to be stuck here until you free up some space on /, or until you think of a way to chroot yourself in /extra. There are guides floating around on the internet on how to do that, since I've never actually done this myself.

That said, if you're using LVMs, you could resize / so that it's big enough to install some things on. However I don't think your setup has an LVM.

Also, I don't believe Yum can do relocatable packages (at least I've never needed to, someone feel free to correct me), and in this case it wouldn't matter until you at least free some space up on /. You could do a du -sch / to find begin finding out which directories you can delete from, though I don't think this would help since your / partition is small enough to presume that it's a basic install with a GUI on top.