Answer: It's unfortunate, but sometimes the branches get so heavy that they break off at one of the junctions. You should be able to root the severed pieces. Allow the end to callous over, then bury it about one-inch deep in sandy (cactus) potting soil. Moisten the soil and keep the plant out of direct sunlight. New roots should form in 2-3 months. You'll be able to tell your plants have successfully rooted when you see new growth. Good luck with your Christmas cactus!
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