Old English ruh "rough, coarse (of cloth); hairy, shaggy; untrimmed, uncultivated," from West Germanic *rukhwaz "shaggy, hairy, rough" (source also of Middle Dutch ruuch, Dutch ruig, Old High German ruher, German rauh), from Proto-Germanic *rukhaz, perhaps from PIE *reue- "to smash, knock down, tear out, dig up" (source also of Sanskrit ruksah "rough;" Latin ruere "to rush, fall violently, collapse," ruina "a collapse;" Lithuanian raukas "wrinkle," rukti "to shrink").
The original -gh- sound was guttural, as in Scottish loch. Sense of "approximate" is first recorded c. 1600. Of places, "riotous, disorderly, characterized by violent action," 1863. Rough draft is from 1690s. Rough-and-ready is from 1810, originally military; rough-and-tumble (1810) is from a style of free-fighting.