"underground part of a plant," late Old English rot, from a Scandinavian source akin to Old Norse rot "root," figuratively "cause, origin," from Proto-Germanic *wrot (source also of Old English wyrt "root, herb, plant," Old High German wurz, German Wurz "a plant," Gothic waurts "a root," with characteristic Scandinavian loss of -w- before -r-), from PIE root *wrād- "branch, root." The usual Old English words for "root" were wyrttruma and wyrtwala.
Figurative use is from c. 1200. Of teeth, hair, etc., from early 13c. Mathematical sense is from 1550s. Philological sense from 1520s. Slang meaning "penis" is recorded from 1846. In African-American vernacular use, "a spell effected by magical properties of roots," 1935. To take root is from 1530s. Root beer, made from the extracts of various roots, first recorded 1841, American English; root doctor is from 1821. Root cap is from 1875.