They will actually grow with roots attached, and it sort of depends. To take them off yourself you kind of have to mutilate the parent stalk. It'll live, but it will look funny. But, if you're taking them off yourself, you really want to make sure you keep the roots for the babies because, after all, that's what you're after!
If you can wait long enough, and it's hard to be that patient, they will eventually just detach on their own. At this point, you can capture and plant the new stalks.
It's very easy...of course, that's what makes it a weed! lol