Answer: Palms like having their roots crowded so unless the roots are tightly wound around the bottom of the pot, you can repot into the same size pot. If the roots are too cramped, cut off the bottom part of the root ball to encourage new root development and repot into one size larger pot. Use a fairly heavy, coarse soil with plenty of organic matter. A good recipe consists of 4 parts topsoil, 2 parts coarse sand, 2 parts leaf mold or peat moss, and 1 part dried cow manure. Pack the medium firmly around the roots.
After repotting, shade the plant from sun, keep in a warm location out of drafts, and mist regularly for several weeks. Water the plant until the excess drips from the bottom of the container and then don't water again until the top inch or so of the soil is dry.
Eventually you could move the palm outside in a shady, nonwindy location, but gradually acclimate the plant to outdoors.
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