You can :
Add hard disk
Move mysql DB files to other FS (in your case you have just /home FS left )
You can resize your LVM volume to make /home smaller and / bigger (be sure to have backup of course :) )
This option is most straight forward, but LVM strongly recommend to backup your data before resizing
UPDATE (based on comment)
if I add hard disk what must I adjust on my mysql setting to expand
the data to the hard disk? If option to mean I have to move mysql over
what steps need to be taken for that?
- Stop mysql
- Open /etc/my.cnf and find datadir= - here are your mysql datafiles
- Copy/Move them over to your new desired location
- Update datadir= with your new path
- Start Mysql
- Take a beer or whatever you want, cause you are done
How tough to expand the /root?
Read the link above which I already posted.Step by step guide is included there with comprehensive explanation.
Normally what the home partition is to store? Any important files?
It contain user files and setting.Eg your desktop etc.
For system healt /home is not important and can be remounted anytime.