Trees have a vast network of roots which perform different vital functions for the tree and range from non-woody roots only 0.2mm/0.008in in diameter to large, woody roots up to 30cm/12in in diameter. 99% of the roots are actually located in the top 3ft of soil, where there is the most oxygen, nutrients, and moisture to absorb. The major roots branch out horizontally up to 15ft from the trunk of the tree. These roots support a system of framework roots which can be 4-7 times the diameter of the above-ground branch system of the tree! That means a mature Oak tree with a 40ft diameter branch system could have a root system up to 280ft in diameter!
Trees also rely on symbiotic relationships with fungi for their health. Listen to this RadioLab podcast for a compelling story about the hidden world of mycorrhiza beneath our feet.
As is evident in these images - roots are opportunistic and capable of growing in surprising conditions. Have you seen any interesting root formations recently?
Perry, Thomas O. "Tree Roots: Facts and Fallacies." Journal of Arboriculture 8 (1982): 197-211. Web. 19 July 2016