If you have never set a root password for MySQL server, 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 the following command:
$ mysqladmin -u root -p'oldpassword' password newpass
For example, If the old password is abc, you can set the new password to 123456, enter:
$ mysqladmin -u root -p'abc' password '123456'