Sorry, but I have to ask: why increase the root to such a large size if it's more sensible to create new logical volumes for those directories using the most space, eg /usr or /opt?
If you
really need to increase the root filesystem itself:
- Take a backup!
- Verify that backup!
- Do not continue unless you did both steps!
- Increase the size of the LVOL
- Reboot into single-user mode
- Resize with the tool appropriate to your filesystem (ext2resize for Ext2/Ext3, resize_reiserfs for ReiserFS, xfs_growfs for XFS, mount -o remount,resize / for JFS)
- Reboot and verify everything is still working
- Do not throw away your backup until you're absolutely sure everything works