The Problem

I am running Ubuntu 18.04 and I have installed MySQL recently. I have never actually used it yet though. As far as I remember, I never set any password for any user. (If I did, I know what it would be.)

Today I installed phpMyAdmin and found that I was unable to log in to root through phpMyAdmin. I tried to log in to MySQL directly via the terminal without a password:

mysql -u root

And with the password that I would have set, if I forgot:

mysql -u root -p

But both of these returned

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

Attemted Solutions

Attempt 1

I tried following this guide, I stopped the MySQL demon process, I then started the mysqld daemon process using the --skip-grant-tables option. Then when running this command to log in without the password:

mysql -u root

Instead of arriving at the mysql> prompt, I was faced with the following error:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket 
'/var/run/mysqld/mysqld.sock' (2)

Attempt 2

I tried to uninstall MySQL using:

sudo apt-get --purge remove mysql-server mysql-common mysql-client

And then I tried to reinstall MySQL using this command:

sudo apt-get install mysql-server mysql-common mysql-client

And then tried to set a password like this:

mysqladmin -u root password my-new-password

Yet I was once again stumped with an error message:

mysqladmin: connect to server at 'localhost' failed
error: 'Access denied for user 'root'@'localhost''

My fellow programmers, I am absolutely clueless as to where to head from here in the continuation of my quest to obtain the powers of MySQL...

Edit

After using sudo (as per vidarlo's answer) I was able to access my databases, and I managed to change my password using this:

mysql> update user set authentication_string=password("Z4hVdwn9qZ") 
       where user='root';
Query OK, 1 row affected, 1 warning (0.01 sec)
Rows matched: 1  Changed: 1  Warnings: 1

But phpMyAdmin still won't log in and returns the error

#1698 - Access denied for user 'root'@'localhost'