Recently I had the issue, that my root partition (/ or slash) was a bit too small for some update. So I had to look up how to resize the root partition. Luckily with LVM/btrfs this works like a charm (if you added enough free space):

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christian:(hans.heimdaheim.de) PWD:/
Fri Mar 11, 07:02:40 [0] > df -h
Filesystem            Size  Used Avail Use% Mounted on
udev                  2.0G  4.0K  2.0G   1% /dev
tmpfs                 396M  428K  395M   1% /run
/dev/dm-1             952M  789M  176M  82% /
none                  4.0K     0  4.0K   0% /sys/fs/cgroup
none                  5.0M     0  5.0M   0% /run/lock
none                  2.0G     0  2.0G   0% /run/shm
none                  100M     0  100M   0% /run/user
christian:(hans.heimdaheim.de) PWD:/
Fri Mar 11, 07:02:46 [0] > lvextend /dev/vg0/slash -L2G
  Extending logical volume slash to 2.00 GiB
  Logical volume slash successfully resized
christian:(hans.heimdaheim.de) PWD:/
Fri Mar 11, 07:04:51 [0] > btrfs filesystem resize max /
Resize '/' of 'max'
christian:(hans.heimdaheim.de) PWD:/
Fri Mar 11, 07:04:55 [0] > df -h
Filesystem            Size  Used Avail Use% Mounted on
udev                  2.0G   12K  2.0G   1% /dev
tmpfs                 396M  440K  395M   1% /run
/dev/dm-1             2.0G  647M  1.4G  32% /
none                  4.0K     0  4.0K   0% /sys/fs/cgroup
none                  5.0M     0  5.0M   0% /run/lock
none                  2.0G     0  2.0G   0% /run/shm
none                  100M     0  100M   0% /run/user