Answer: Roebelenii is a date palm and the common name of your plant is Pygmy Date Palm. It's a slow-growing plant to about 3' tall, with very narrow leaflets. Palms of all kinds thrive in average household temperature (minimum 50F in winter), moderate light, slightly moist soil, and occasional misting if the room is heated. Palms don't like to be disturbed, so don't repot your palm until it has really outgrown its container.
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