If you have never set a root password for MySQL, the server does not require a password at all for connecting as root.
To setup root password for first time, use mysqladmin command at shell prompt as follows:
$ mysqladmin -u root password NEWPASSWORD
However, if you want to change (or update) a root password, then you need to use following command
$ mysqladmin -u root -p’oldpassword’ password newpass