With a horseshoe you cannot go wrong, Mieko!
I did not see the herbaceous root in the 1st division clearly - just the dark part, but the 2nd root striped dark part is obvious. I agree with Liz your 3rd division looks like TP as well. Good luck!
Personally I would probably try to get rid of any herbaceous roots before planting new divisions. Liz could be right on the 1st one and those 2 white sprouts on the left and right side are herbaceous growth? You have to look at it again...
