Became interested when it sat at the top for days. Most cacti require little more than a medium to root in and little water. it takes a long time

Chop it, dust the ends with something, and leave it somewhere it won't parch. There's a huge window of opportunity between the root tips forming and the root stubs dehydrating, so don't feel compelled to examine the cut end more than once a month.

For the 'something', sulphur is a common wound treatment because of its anti-fungal properties. Ground cinnamon is also suggested, but I've found it to take on too much water. My current treatment of choice is Polyfilla. It dries the wound nicely (physically removing the water that pathogens need) and if you can get enough on to form a solid cap, you have something that protects the cut end and pops off by itself once the roots grow sufficiently.