How to give user root permissions?

You should read the Arch Wiki page on sudo.

sudo ("substitute user do") allows a system administrator to delegate authority to give certain users (or groups of users) the ability to run some (or all) commands as root or another user while providing an audit trail of the commands and their arguments.

You can install sudo from the repositories and then configure it to allow your user, jack, access to privileged commands by editing /etc/sudoers. Make sure you do this using the visudo command.

To give the user jack full root privileges, you would add this line:

jack ALL=(ALL) ALL

What I usually do is enable root privileges for a specific group. That way you can just add users you want root privileges to that group.

Edit /etc/sudoers with visudo and add (or comment out):

%wheel      ALL=(ALL) ALL

Then add your user to that group:

gpasswd -a jack wheel