Palm tree roots tend to be fairly shallow when compared to the height of the tree. Despite urban legends to the contrary, palm tree roots do not equal the height of the tree. Instead, they grow in a root ball.
Palm tree roots do not widen out as they grow; rather, they tend to grow straight down. As a result, they are unlikely to damage nearby sidewalk or pavement. Palm tree roots regularly regenerate from the root ball. Since they are always regenerating and dying off, they do not grow very long. Palms have no tap root. Instead, their roots jut out from the root ball in all directions, drawing nourishment and water from a wide swath of ground.