There is a balance between nice sprouts and sprouts on steroids. The overly fertilized ones can be too fat. Too much of a good thing can be a bad thing and that is really true with fertilizer. I do put some in the water but not too much. There are lots of other questions you have not asked " How much do you water the pot tubers?, What temps are best for sprouting pot tubers? , How much light is needed for nice sprouts? How do you know the pot tuber is too tired to produce any more cuttings AND will stay alive to plant in the ground? Should I sprout tubers in a flat of potting soil without individual pots? Can I leave the tuber eye above the soil level so I can see it better or is that not a good practice? Should I use a scalpel, scissors or bonsai scissors or my fingers to remove sprouts? What is the success rate for cuttings that already have white roots attached? How much light in lumens is needed to root cuttings and should the lights be on 24 hours a day or perhaps 12 hours per day? Why is rooting in a greenhouse much, much more difficult as compared to inside using lights.? Which rooting mediums work well: mineral wool, oasis wedges, sharp sterile sand, soil from the garden sterilised by baking, perlite, vermiculite, water with or without a bubbler mechanism, germination soil mix with peat moss , ?,. I know people who have used all of these mediums successfully. The questions can go on and on 
I am sure I missed some of them.
