Answer: Root growth and development depends a great deal on the soil type and environmental conditions the plant experiences. As a general rule of thumb, roots extend out as far as the dripline of the canopy of a tree or shrub and are concentrated in the top 8-18" of soil. Some very large trees with wide canopies (such as maples and oaks) can have surface roots extending out about twice as far as the diameter of the canopy. The tropical plants you list will have similar root system growth; 8-18" in depth and about as far out as the longest branches, stems or fronds.
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