restroom n.

[sleep, repose, slumber] Old English ræste, reste "rest; a bed or couch; intermission of labor; mental peace, state of quiet or repose," from Proto-Germanic *rasto- (source also of Old Saxon resta "resting place, burial-place," Dutch rust, Old High German rasta, German Rast "rest, peace, repose"), a word of uncertain origin.

The original prehistoric signification of the Germanic noun was perhaps a measure of distance; compare Old High German rasta, which in addition to "rest" meant "league of miles," Old Norse rost "league, distance after which one rests," Gothic rasta "mile, stage of a journey." If so, perhaps a word from the nomadic period. But if the original sense was "repose," the sense was extended secondarily to "distance between two resting places."

Sense of "absence or cessation of motion" is from late 15c. The meaning "that on which anything leans for support, thing upon which something rests" is attested from 1580s, with specific senses developing later. In music, "an interval of silence," also the mark or sign denoting this, 1570s.

At rest "dead" is from mid-14c., on the notion of "last rest, the big sleep, the grave." The roadside rest stop for drivers on busy highways is by 1970. The colloquial expression give (something) a rest "stop talking about it" is by 1927, American English.

[R]est and repose apply especially to the suspended activity of the body ; ease and quiet to freedom from occupation or demands for activity, especially of the body ; tranquility and peace to the freedom of the mind from harassing cares or demands. [Century Dictionary]

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.