Which SQL Server system database is more important:
resource database is damaged, can the database engine work?
Can the system work with only the
master database? If not, which system databases are necessary?
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Both the master and resource DB is important.
If the master DB becomes corrupt, you can still restart your server by creating a new master DB. You will loose your server principals and other data that are stored in the master, but at least you will be up and running. Once you recreate your logins (hopefully these were scripted) then you have access to your data.
The resource DB contains the sys schema. I am not sure if you can just copy these from another instance if there are not much changes done to these. Will have to see if there is anybody else who had this issue.
They are both 100% required. However, mssqlsystemresource is read-only, and specific to your version/patchlevel, so it's easy to restore, in theory.