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
For example, If old password is abc, and set new password to 123456, enter:
mysqladmin -u root -p'abc' password '123456'