Answer: You didn't describe the damage so I'm going to guess your radishes have little tunnels through them. This is the most common type of problem with radishes. The worms are the larvae of a fly so control is really difficult. The adult fly lays eggs on the top surface of the radish, or on the soil next to the radish. When the eggs hatch, the larvae tunnel through the radish, feeding on the flesh. When they've had enough to eat they pupate, then fly away.
The best control is to place a barrier between your radishes (and carrots, too!) so the adults cannot lay eggs in and around your crops. A floating row cover carefully anchored at soil level will keep your crops safe from invasion. Row covers come in various lengths and are sturdy enough to use over and over again. I think your root crops are good candidates for this type of pest control.
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