I've been here 11 years now and the horseradish patch is no bigger than before. It gets lots of water and seems very happy under the apple trees, but it's also surrounded by (and by late summer, overtopped by) long grass.
However, the rhubarb... I started with one plant. Canadian Red. It did not like where I first put it ... died back in June and I thought it had croaked. Next year there it was again, so I dug it up and moved it, but in the process broke the root into 3 pieces. Decided the next spot was in the way so I dug up them up to move again... one root was the size of your leg... and they broke again, and now I have 12. They haven't spread by root beyond where they are, but I sometimes let one bloom, and I get seedlings anywhere it's a bit shady and damp. The ground around its fence-shaded spot gets quite hot and dry, which probably discourages it from spreading further. (Definitely benefits from afternoon shade.)
I didn't pay any attention to root taper, I just made a ditch and dropped them in and covered them up. They seem to have paid no attention to where they started, and came up randomly kinda all over the designated area. And I moved them during June, and it was already hot. Apparently the sole required criterion is "piece of root, buried any which way".
If the roots have grown apace with after the first move, moving 'em again might need a backhoe. I'm afraid to dig down and look.
Side note: rhubarb sauce is wonderful on pork, chicken, and even beef!! (I add lemon pepper, too.) And you can mix it with chili sauce for a unique sweet-and-sour BBQ sauce.