The tried methods all prompt similar errors
ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that
corresponds to your MySQL server version for the right syntax to use near '("123456") where user="root"' at line 1
Update user statement
UPDATE user SET password=PASSWORD('123456') WHERE user='root';
FLUSH PRIVILEGES;
Set password statement
SET PASSWORD FOR root=PASSWORD('123456');
authentication_string change
update mysql.user set authentication_string=password('123456') where user='root' ;
Final solution
mysql> SET PASSWORD = '123456';