Middle English roum, from Old English rum "space, extent; sufficient space, fit occasion (to do something)," from Proto-Germanic *ruman (source also of Old Norse, Old Saxon, Old High German, Gothic rum, German Raum "space," Dutch ruim "hold of a ship, nave"), nouns formed from Germanic adjective *ruma- "roomy, spacious," from PIE root *reue- (1) "to open; space" (source also of Avestan ravah- "space," Latin rus "open country," Old Irish roi, roe "plain field," Old Church Slavonic ravinu "level," Russian ravnina "a plain").
Old English also had a frequent adjective rum "roomy, wide, long, spacious," also an adverb, rumlice "bigly, corpulently" (Middle English roumli).
The meaning "chamber, cabin" is recorded by early 14c. as a nautical term; applied by mid-15c. to interior division of a building separated by walls or partitions; the Old English word for this was cofa, ancestor of cove. The sense of "persons assembled in a room" is by 1712.
Make room "open a passage, make way" is from mid-15c. Room-service is attested from 1913; room-temperature, comfortable for the occupants of a room, is so called from 1879. Roomth "sufficient space" (1530s, with -th (2)) now is obsolete.
"to occupy a room or rooms" (especially with another) as a lodger," by 1825 (implied in roomed), from room (n.). Related: Rooming. Rooming-house, "house which lets furnished apartments," is by 1889, according to OED "chiefly U.S." In Old English (rumian) and Middle English the verb meant "become clear of obstacles; make clear of, evict."