MYSQL Issue:- ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)

[root@servert1 ~]# /etc/init.d/mysqld stop
Stopping MySQL: [ OK ]
[root@servert1 ~]# mysqld_safe --skip-grant-tables &
[1] 13694
[root@servert1 ~]# Starting mysqld daemon with databases from /var/lib/mysql

root@servert1 ~]# mysql -u root
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 1
Server version: 5.0.77 Source distribution

Type 'help;' or '\h' for help. Type '\c' to clear the buffer.
mysql> update user set password=PASSWORD("testpass") where User='root';
ERROR 1046 (3D000): No database selected
mysql> show databases;

+--------------------+
| Database |
+--------------------+
| information_schema |
| mysql |
| test |
+--------------------+
3 rows in set (0.13 sec)
mysql> use mysql; 
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Database changed
mysql> show tables;
+---------------------------+

| Tables_in_mysql |
+---------------------------+
| columns_priv |
| db |
| func |
| help_category |
| help_keyword |
| help_relation |
| help_topic |
| host |
| proc |
| procs_priv |
| tables_priv |
| time_zone |
| time_zone_leap_second |
| time_zone_name |
| time_zone_transition |
| time_zone_transition_type |
| user |
+---------------------------+
17 rows in set (0.00 sec)


mysql> update user set password=PASSWORD("testpass") where User='root';
Query OK, 3 rows affected (0.05 sec)
Rows matched: 3 Changed: 3 Warnings: 0

mysql> flush privileges;
Query OK, 0 rows affected (0.04 sec)

mysql> quit
Bye
[root@servert1 ~]# /etc/init.d/mysql restart
bash: /etc/init.d/mysql: No such file or directory
[root@servert1 ~]# /etc/init.d/mysqld restart
STOPPING server from pid file /var/run/mysqld/mysqld.pid
101120 04:17:15 mysqld ended
Stopping MySQL: [ OK ]
Starting MySQL: [ OK ]

[1]+ Done mysqld_safe --skip-grant-tables
root@servert1 ~]# mysql -u root -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 2
Server version: 5.0.77 Source distribution
Type 'help;' or '\h' for help. Type '\c' to clear the buffer.


mysql> quit
Bye