I appreciate it might seem like semantics to you, but .... your use of 'root' above is confusing.
What's worse, I think I will find it hard to explain ....
what is commonly referred to as 'root' can have two meanings; the first refers to the administrator privileges, or root privileges. So when you are told to 'su to root', that means to elevate your privileges to those of the administrator, to do something that needs those privileges.
root is also used to refer to the filesystem which holds the operating system; so when a reference is made to the 'root partition' it is the partition that holds the currently running
OS that is being referenced.currently running
....... is most important here. When operating from a liveCD your currently running
root partition is not on the hard drive, and so the partition on the HDD is not referred to as root in that situation.
So the /dev/sdXy notation is used to designate partitions which are not part of the presently running operating system.
I hope that did not confuse things even more.
Now, to apply the above ....
I ~can~ unmount root?
No, you cannot unmount the OS you are running, but you can unmount the partition that the HDD install uses as its root partition ..... and all other unneeded partitions too, by using the umount -a
command. This will tell you it cannot unmount its own root, but all unnecessary partitions will be unmounted. (The -a option means ALL)
Please take note of the spelling of the command .... it is not un
mount as you posted, but umount.
I would suggest you also use the -v option in fsck, to get a report of what it found etc. and save that report. Such a report may be useful when making decisions about the HDD.