Arch root partition is full, how to clean it up?

After installing pacman packages (last one was 'ungoogled-chromium') my root partition of 20GB is completly full. Now I can't update new packages.

My partition structure is: root (20GB) /home (470GB) swap (10GB)

How can I delete the garbage that is piling up in my root, and how to prevent it from happening again.

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Thanks! This realy helped me out. Saved 1GB on my root.

When I install things with pacman, is it storing files in the root partition? If so, can I specify installations to install inside the home partition?

Pacman installs binaries in the root partition because they are installed system-wide. I don't think that pacman can install binaries for a single user (inside the home partition).

One way of achieving that would be compiling or downloading the binaries manually as a normal user and putting the .desktop file in .local/share/applications. The program would then be only accessible for a single user though.