
chirurgisch
surgical
Relating to surgery; carried out by means of an operation.
Der Tumor musste in einem chirurgischen Eingriff entfernt werden.
The tumor had to be removed in a surgical procedure.
surgical
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surgical
Relating to surgery; carried out by means of an operation.
Der Tumor musste in einem chirurgischen Eingriff entfernt werden.
The tumor had to be removed in a surgical procedure.

surgical
Figuratively: extremely precise and exact, as in the work of a surgeon.
Mit chirurgischer Präzision zerlegte der Uhrmacher das winzige Uhrwerk.
With surgical precision, the watchmaker dismantled the tiny clockwork mechanism.
The adjective 'chirurgisch' (surgical) is derived from the noun 'die Chirurgie' (surgery). The ending '-isch' (-ic/-ical) is a typical ending used to form an adjective from a noun.
Die chirurgische Abteilung des Krankenhauses ist sehr modern.
The hospital's surgical department is very modern.
You can recognize the meaning from the context. If people are talking about medicine, operations, or doctors, the literal meaning is intended. In other contexts that require accuracy, the figurative meaning is intended.
Für diese Operation braucht man ein chirurgisches Skalpell.
You need a surgical scalpel for this operation.
In a medical context, 'chirurgisch' (surgical) is often combined with certain nouns. Common combinations are 'chirurgischer Eingriff' (surgical procedure), 'chirurgische Behandlung' (surgical treatment), or 'chirurgische Instrumente' (surgical instruments).
Nach dem Unfall war ein kleiner chirurgischer Eingriff notwendig.
After the accident, a small surgical procedure was necessary.
In the figurative meaning, the word is almost always used in the fixed expression 'mit chirurgischer Präzision' (with surgical precision) or 'mit chirurgischer Genauigkeit' (with surgical accuracy). It describes an extremely exact approach.
Mit chirurgischer Präzision setzte er das Modellauto zusammen.
With surgical precision, he assembled the model car.
operational / surgical
When describing medical treatment, operativ and chirurgisch can both refer to an operation. Operativ generally emphasizes that the treatment is carried out through surgery. Chirurgisch focuses more on the connection with surgery or on the nature of the procedure.

Die chirurgische Behandlung des komplizierten Bruchs übernimmt ein spezialisiertes Team.
A specialized team is taking over the surgical treatment of the complicated fracture.
Die Ärzte behandeln den komplizierten Bruch operativ.
The doctors are treating the complicated fracture surgically.