If you have that same problem in MySql 5.7.+ :
 
it's because MySql 5.7 by default allow to connect with socket, which means you just connect with
    
Access denied for user 'root'@'localhost'it's because MySql 5.7 by default allow to connect with socket, which means you just connect with
sudo mysql. If you run sql :SELECT user,authentication_string,plugin,host FROM mysql.user;+------------------+-------------------------------------------+-----------------------+-----------+
| user             | authentication_string                     | plugin                | host      |
+------------------+-------------------------------------------+-----------------------+-----------+
| root             |                                           | auth_socket           | localhost |
| mysql.session    | *THISISNOTAVALIDPASSWORDTHATCANBEUSEDHERE | mysql_native_password | localhost |
| mysql.sys        | *THISISNOTAVALIDPASSWORDTHATCANBEUSEDHERE | mysql_native_password | localhost |
| debian-sys-maint | *497C3D7B50479A812B89CD12EC3EDA6C0CB686F0 | mysql_native_password | localhost |
+------------------+-------------------------------------------+-----------------------+-----------+
4 rows in set (0.00 sec)ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'Current-Root-Password';
FLUSH PRIVILEGES;+------------------+-------------------------------------------+-----------------------+-----------+
| user             | authentication_string                     | plugin                | host      |
+------------------+-------------------------------------------+-----------------------+-----------+
| root             | *2F2377C1BC54BE827DC8A4EE051CBD57490FB8C6 | mysql_native_password | localhost |
| mysql.session    | *THISISNOTAVALIDPASSWORDTHATCANBEUSEDHERE | mysql_native_password | localhost |
| mysql.sys        | *THISISNOTAVALIDPASSWORDTHATCANBEUSEDHERE | mysql_native_password | localhost |
| debian-sys-maint | *497C3D7B50479A812B89CD12EC3EDA6C0CB686F0 | mysql_native_password | localhost |
+------------------+-------------------------------------------+-----------------------+-----------+
4 rows in set (0.00 sec)sudo mysql_secure_installation command.