mysqldump: Got error: 1698: "Access denied for user 'USER'@'localhost'" when trying to connect code example

Example 1: ERROR 1698 (28000): Access denied for user 'root'@'localhost'

>>> sudo mysql -u root -p

>>> USE mysql;

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

>>> FLUSH PRIVILEGES;

>>> exit;

>>> service mysql restart;

Example 2: ERROR 1698 (28000): Access denied for user 'root'@'localhost'

$ 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