Hello 4joey1,
In addition to all the good advice given above I might throw in some remarks, because my idea is that you have some misconseptions. When I am wrong, I do appoligize.
The root partition has nothing to do with the user root (except for their shared name). The root partition is the disk partition that is mounted on /. And that is at the root of the Unix/Linux directory tree. You do not need a password to read and/or write there.
You do need the root password when you want to access directories/files that are not owned by you, but by root (and root not giving the allowance to do the r/w by e.g. setting the access bits for 'world').
Now when you have a seperate /home partition, most directories/files that are on the / filesystem are owned by root and not writable by normal users. This is because of ownership and access bits, not because of them being on the root filesystem.
Back to your problem.
I understand that your /home partition is getting full, but that your / partition is still having space enough. Apart from the tedious task of shrinking/expanding filesystems, a (maybe only temporary) solution might be found by using space on / for part of your user files and making a symbolic link to it.
Example. User happy is running out of space and gathers a lot of music file in /home/happy/Music/. We want to move this to the root partition so that more music can be added and also more space for others things becomes available on /home/happy/.
As root create a directory on the root partition and make happy the owner:
Code:
mkdir /happy-needs-more-space
chown happy:users /happyneeds-more-space
Now happy can do:
Code:
cd # to your home directory
mv Music /happy-needs-more-space/ #takes some time because it will copy all music
ln -s /happy-needs-more-space/Music Music #makes the link from your well know place to where it is now
And happy is back into bussiness.
I hope you get the principle behind it. Of course after this your root partition does contain userdata and this should be taken into acount when installing a new system.