'Rural' is Latin for 'of the countryside' — from 'rus' (open land). Same PIE root as 'room.'
Of, relating to, or characteristic of the countryside rather than the town; living in or associated with agricultural areas.
From Old French 'rural' (of the countryside), from Latin 'rūrālis' (pertaining to the country), from 'rūs' (genitive 'rūris,' the country, open land, a farm, an estate), from PIE *rewh₁- (to open, to open up space), which conveyed the concept of wide, open land. This PIE root connects 'rural' to an unexpected family of English words: 'room' (from Old English 'rūm,' spacious area, via Proto-Germanic *rūmą from the same PIE root), and German 'Raum' (space, room). The semantic thread is 'open space' to 'countryside' (in Latin)