After a Live Media installation, the root password is initially set to the same password as the user account that is created during installation. Because it is created in an expired state, the first time you assume the root role, you should authenticate using your own password. At this point, a message indicates that the password for the user root has expired and you will be requested to provide a new one.
If you are prompted to assume the root role after starting an administrative command from a GNOME menu item, you will be prompted to supply a new root password. If you are using the su command to assume the role, the command sequence is as follows:
$ su Password: su: Password for user 'root' has expired New Password: Re-enter new Password: su: password successfully changed for root.