ANSWER:

I think it will be a bad idea to give him root password if you don’t trust him. When he gets the password he can do whatever he wants.

What if he just changed root password before you can even notice that.

To answer your question about monitoring the user activity, you can try whowatch. It can show you the logged in users and the processes they are running. However, you may not be able to notice a quick commands like doing ls in a small directory.

by Khaled from http://serverfault.com/questions/382866