I have never planted root vegetables before so I don't know how to tell whether it is ripe or not without pulling the root out of the soil and seeing it.
I love beets and I love carrots also but if I ever grow them, I am going to have to know when they are ripe without pulling them out of the soil. One solution I can see to this is hydroponics where you grow plants in nutrient enriched water. There is just one problem with that. Roots, whether you are talking about the edible roots or the non-edible roots, need oxygen and the little bit of oxygen that is dissolved in water is not enough. However too much oxygen can kill the plant if it isn't doing cellular respiration fast enough.
So how would I know when a beet or a carrot or any other edible root is ripe without pulling the root out of the soil or risking lack of oxygen and oxygen poisoning with hydroponics?