How can I check for free RAM slots without opening my computer case?

Download CPU-Z (free, tiny, no bloat), open it, and go to the SPD tab. It lists every slot on your motherboard — if only one slot shows data, you have a free slot; if both show data, you’re full and need to replace sticks. For desktops this is instant, no screwdriver needed. Laptops are trickier since some have soldered RAM that CPU-Z can’t see.