Got error: 1698: Access denied for user 'root'@'localhost' when trying to connect

>>> sudo mysql -u root -p

>>> USE mysql;

>>> UPDATE user SET plugin='mysql_native_password' WHERE User ='root';

>>> FLUSH PRIVILEGES;

>>> exit;

>>> service mysql restart;
$ sudo mysql -u root # I had to use "sudo" since is new installation

mysql> USE mysql;
mysql> UPDATE user SET plugin='mysql_native_password' WHERE User='root';
mysql> FLUSH PRIVILEGES;
mysql> exit;

$ service mysql restart