I would like to increase root partition from another partition so that I can save more documents in Home and Desktop. whether it is possible without formating root partition if so please explain
this is only possible on the fly with LVM's as the above post suggests.Your root partition should already be an Logical Volume, but there is no more space to increase the volume, so just add a disk, add it to the volume group of root and use lvextend to increase the lvm.
While it never hurts to have a backup, your categorical statement regarding reformatting is incorrect. ext2, ext3, ext4, xfs, btrfs can all be grown (even while mounted, with >= 2.6 kernels). Perhaps other filesystems can be grown as well, but I did not check.
Obviously, if the filesystem currently occupies the full partition, the partition itself needs to be redefined. However, this is not a destructive operation; it merely modifies a value in the partition table. The partition starting point must obviously be preserved.
I agree with this, but it's not something with which I ever concern myself for personal systems. I prefer the simplicity of one large partition. For a production machine, however, it's useful to be able to tune filesystems to their function (small number of large files or large number of small files?) and to mount each with as many restrictions as possible (noexec, nosuid, nodev, etc).
I think it's especially vital for personal systems. You don't need 5 little fiddly partitions, but having just two can save you a lot of trouble. If your machine gets hard powered off or crashes for whatever reason, disk corruption tends to land wherever it's busy writing. You wouldn't let that happen much to a production machine but it happens to a personal computer a lot.
Separate root means it can begin booting, see that /home needs fsck-ing and do so and get on with its business.
All one glob means kernel panic, you need a recovery CD to fix it.
While I use Linux daily, I don't use it heavily and I do not consider myself expert in its internals. I have an obsolete Debian installation on obsolete hardware. I use it almost everyday to quickly test code for portability, but I have not installed a Linux distribution in 7 years (discounting test driving the occasional livecd).
My linux machine uses three hard disk partitions: /, /home, and swap. Admittedly, that's not quite the one large partition scenario I mentioned in my previous post, but it's close. Most disk activity is confined to the root partition. There's not much going on in /home, aside from creating a few files a day, and having the shell write to its history file. I don't use X, just a the virtual text consoles. The machine never swaps (I'd know if it was thrashing). However, the system startup scripts start mysqld, lighttpd, memcached, and php. They generate quite a bit of activity on the root partition (/var mostly).
At least several times a month, in a hurry I force a hard shutdown (it's 15 yr old hardware). At other times, adverse weather causes a reboot (brown out without UPS). Still, in 7 years, the machine has never failed to reboot (although, obviously, it may have to fsck).
I also do the same with a Windows XP laptop. Never had any issues rebooting or losing data (after having closed all documents and apps except the web browser with its session management).
Perhaps I've been uncommonly lucky. Which, I may be. In 25 years, I've never experienced a personal hard drive failure <knock on wood>.
I will continue to tempt the fates until they bite me.