Access denied for user 'root'@'localhost' (using password: NO)

/etc/init.d/mysqld stop
mysqld_safe --skip-grant-tables & mysql -u root
mysql> use mysql;
mysql> update user set password=PASSWORD("newrootpassword") where User='root';
mysql> flush privileges;
mysql> quit
/etc/init.d/mysqld stop
/etc/init.d/mysqld start