Tree trunks sprout branches after their tops have been cut because they still have roots to provide moisture and nutrients. Cut Christmas trees cannot regrow their roots. They will simply rot if planted or left in water.
Commercial Christmas trees are cut weeks or months in advance. Dry when purchased, they may suck up buckets of water once a thin layer is cut from the trunk. This allows the needles to remain on the tree -- it does not mean the tree is alive.
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A self-cut tree is fresher and retains its needles longer, but won't regrow its roots if planted.
Although difficult, it may be possible to grow cuttings from your Christmas tree. Cut healthy branches the size of a pencil as soon as possible. Dip the cut ends in rooting hormone, plant in potting soil and water well. Keep in a dark, cool spot and check weekly for root growth.
An uprooted live tree placed in a warm, dry home for five weeks will dry out regardless of whether you keep it watered. Keep a live tree indoors for only two weeks. Dig the hole before the ground freezes and plant as soon as possible.