surgical (adj.)

c. 1300, sirgirie, "medical treatment of an operative nature, such as cutting-operations, setting of fractures, etc.," from Old French surgerie, surgeure, contraction of serurgerie, from Late Latin chirurgia "surgery," from Greek kheirourgia, from kheirourgos "working or done by hand," from kheir "hand" (from PIE root *ghes- "the hand") + ergon "work" (from PIE root *werg- "to do").

According to OED, the British sense of "session at which a Member of Parliament (or other public servant) is available locally to be consulted by constituents" is by 1951, from an extended sense in medical practice of "regular session at which a doctor receives patients for consultation" in a room or den set aside for that purpose called a surgery (by 1846). The word has been extended in Britain to other free consultations for advice.

compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)). Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.

Proto-Indo-European root meaning "the hand." 

It forms all or part of: chiral; chiro-; chirognomy; chirography; chirology; chiromancy; chiropodist; chiropractic; chiropractor; chirosophy; chirurgeon; enchiridion; surgeon; surgery; surgical.

It is the hypothetical source of/evidence for its existence is provided by: Greek kheir, Hittite keshshar, Armenian jern "the hand"