Trees with shallow, aggressive root systems are more likely to invade greenhouses than slow-growing trees with deep roots. Problematic trees include silver maples (Acer saccharinum), U.S. Department of Agriculture plant hardiness zones 4 through 9, and poplars, aspen and cottonwoods (Populus spp. and cvs.), hardy in USDA zones 3 through 9. Silver maple is tolerant of root pruning and can be controlled without killing the tree if it is already growing near the greenhouse.
Greenhouse floors can be made from concrete, gravel or bare soil or sand. For greenhouses with dirt or gravel floors, the tree roots can be killed by cutting and digging out the roots. The same method will work for roots that have grown into in-ground beds on the floor of the greenhouse. Be careful when removing roots if preserving the tree is important. If the roots are close to the trunk of the tree or within the crown's drip line, avoid cutting roots that are larger than 1-inch in diameter.
One way to kill tree roots inside a greenhouse and prevent new roots from growing in is to install a root control barrier. The barriers are installed beneath the soil level outside the greenhouse. Digging down to install the barrier will cut through existing roots, killing the ones already inside the greenhouse. Several types of barriers are effective at preventing new roots from growing. Welded fiber or mesh sheets with tiny openings will trap and strangle new root growth. Solid barriers of plastic, wood or metal deflect roots and keep them from growing into the greenhouse.
If the tree roots are causing persistent problems, one solution is to kill the tree. Concrete floors can block weeds and some tree roots, but aggressive roots may crack concrete. In this case, removing the tree and replacing the damaged concrete is an option. After a tree down is cut down, certain species can grow back from the stump and continue feeding the roots. To prevent this, treat the cut stump with a systemic herbicide such as triclopyr or glyphosate. These herbicides can purchased in ready-to-use formulations and sprayed on the bark and surface of the stump right after cutting. If any new shoots appear, spray the leaves with ready-to-use glyphosate.