How do I take care of sprouts for hydroponic growing?

I cut open an old tomato the other day and found that a bunch of the seeds had sprouted! I would like to grow them hydroponically in a nutrient solution without a ‘medium’. I grow some houseplants that way, in jars of solution with a bit of tin foil around the base of the stems to hold them firmly in the top of the jar, so the roots are half in and half out of the water. The sprouts are still a bit small for this, but I don’t really want to put them in dirt because I would like to keep them clean for later. Any suggestions?

How do I take care of sprouts for hydroponic growing?
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