No Edible Roots on Radishes, Beets and Carrots
Start with a soil test. Adding too much nitrogen can encourage all leaves and no sizeable roots. A lack of phosphorous can prevent root development. Most garden soils have enough phosphorous, but your soil may be the exception. The soil test results will tell you what type and amount of fertilizer is needed.
Improve heavy clay soils by working several inches of organic matter into the top 8 to 12 inches of soil. And create a slightly raised planting bed with the existing soil. Both strategies will improve drainage and growing success.
Thin young plantings. Leave enough room between remaining plants for the roots to grow to full size.
A bit more information: Avoid the need to thin plantings with the help of seed tapes. Seeds are secured onto biodegradable tapes at the proper spacing. Or take the sting out of the task by thinking of thinning as a form of harvesting. Use the beet and radish seedlings removed during thinning as sprouts on sandwiches and salads.