The cracking of carrot roots frequently occurs after a period of drought, either natural or man made. Did you go away for a few days and the neighbors kid didn't water the garden like you paid him to, or did he turn it into a pond ? A lack of water followed by a sudden surge of moisture, such as a downpour after a period of drought, or you trying to compensate for low moisture by over watering causes cracking and splitting in carrots and other common veggies as well. Moisture stress not only results in carrots cracking but can also cause stunted poor quality carrots.
Over fertilization, particularly with high nitrogen fertilizer can cause carrots to develop multiple roots and at times crack in the process.
Cracked carrots are generally safe to eat, assuming no secondary opportunistic pathogens invaded the root prior to harvest, It is best to simply cut off the damaged portion. Common sense and a visual inspection should dictate whether the carrot is safe to eat or not.
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