Changed root password from '' to ''. Now cannot connect to databases in Cloud SQL prompt
Login to MySQL using current password and then you can change password like this

mysql&gt; SET PASSWORD FOR root@'localhost'=PASSWORD('');
Query OK, 0 rows affected (0.00 sec)


Now you can login MySQL using BLANK password.

This is not the most secure way to change password for better approach please have a look at How to Reset the Root Password.