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These 3 cacti were all in one pot. I was going to separate them, but I didn't think about the roots. They were growing out the bottom hole.
How can I separate the severely intertwined roots? Will I have to rip them all off? Or should I just not separate them and put it all in one big pot?

You are going to have to rip it somewhat, but I'd suggest starting by filling a bucket with water and submerging the rootball. Try and work out the dirt and at the same time feel if any of the plants is starting to come loose. Often getting rid of the soil helps the roots come apart.

You're gonna need to get rid of that soil anyway, so go for it.

Just take your time. Squeeze the rootball, soak it, get your fingers in there. Be gentle and don't rush it, it won't be as hard as you think. And it doesn't matter if they loose some of the roots. But let it dry before you repot, and no water in the first week or so.

Due to the size I couldn't hold it over a bucket, so I just layed them sideways and poured water over it. Then I put on some disposable gloves and spent an hour or two clearing out the dirt and untangling the larger roots. It was interesting. Ran to Lowes a half hour before it closed to get a few pots, they were out of cactus soil so I got some at Walmart. I finished potting them in the dark by lantern. You can probably tell which three these are in the picture below, the other 4 I potted earlier today. I put an inch or so of pebbles in the bottom of all of them. I will post more pictures and follow-up tomorrow. Unfortunately they're spending the night outside, I hope they don't get too many bugs on them.

Also, unfortunately, before I read your reply HairyHarry, I by habit poured a can of water over then to even out the soil. I will, however, be gone for the next 2 weeks in a few days, so definitely won't be watering them then.

Good, now you should take them all out of those pots and get rid of that soil

By the time you get back, you should know whether the advice not to water newly mangled roots was over-cautious or not It might take longer to realise that the soil needs better drainage.

Just to clarify the last two comments a bit. What you buy in the store called "cactus soil" is terrible and should not be used for any cactus or succulent. The bag is lying to you. Get a bunch of pumice if you can find it (check a real nursery, not a box store) and mix it roughly 70% pumice to 30% the cactus soil you have. If you can't find pumice then perlite will work, it is just very prone to floating which is annoying when you water it.