After installing mysql, you need to create an account to manage your databases as descried in this link. But if you do need to keep root as your databases manager!
Lets do the below steps:
sudo mysql -u root
USE mysql;
UPDATE user SET plugin='mysql_native_password' WHERE User='root';
FLUSH PRIVILEGES;
exit;
After this you can login to your mysql databases and manage them using the root account and phpmyadmin too.
