The correct answer is C) to save American lives.
The option that was a reason President Truman authorized the dropping of the atomic bomb was to save American lives.
Although very controversial, the decision of President Harry S. Truman to dropping of the atomic bomb over two Japanese cities was made to save American lives and force a quick ending of the war. Otherwise, they said, it could be a prolonged armed confrontation with Japanese troops that could risk many lives.
The first nuclear bomb was launched over the city of Hiroshima on August 6, 1945. The second was launched over Nagasaki on August 9, 1945.