Trying to set MySQL root password results in error

I'm still very new to MySQL and Debian, but have been reading a lot during the last days.

I have a root account to a virtual machine that I want to use for Wordpress. One thing I read was that I should password protect MySQL because by default root user doesn't need a password for it.

I read someone doing it like this:

 mysql> mysqladmin -u root password mypassword;

But that gives me the following error:

ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that     corresponds to your MySQL server version for the right syntax to use near 'mysqladmin -u     root password mypassword' at line 1