courtroom (n.)

late 12c., "formal assembly held by a sovereign," from Old French cort "king's court; princely residence" (11c., Modern French cour), from Latin cortem, accusative of cors (earlier cohors) "enclosed yard," and by extension (and perhaps by association with curia "sovereign's assembly"), "those assembled in the yard; company, cohort," from assimilated form of com "with, together" (see com-) + stem hort- related to hortus "garden, plot of ground" (from PIE root *gher- (1) "to grasp, enclose").

Both senses of the Latin word emerged in English. From the purely physical sense come "palace, residence of a sovereign" (c. 1200), "enclosed space connected with a building or buildings" (early 14c.), and the sporting sense "smooth, level plot of ground on which a ball game is played" (1510s, originally of tennis). Also "short arm of a public street, enclosed on three sides by buildings" (1680s), formerly noted for poverty or as business districts.

From the notion of "surroundings of a sovereign in his regal state" (c. 1200) comes the legal meaning "a tribunal for judicial investigation" (c. 1300, early assemblies for justice were overseen by the sovereign personally), also "hall or chamber where justice is administered" (c. 1300). As an adjective, "pertaining to a court," late 13c.

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 Roomth "sufficient space" (1530s, with -th (2)) now is obsolete.