Given the possible outcomes of the Pacific War, the dropping of the atomic bombs is justifiable. The United States had pushed the Japanese back to their archipelago. This was a long and bloody campaign of Island Hopping that cost the US 100,000 soldiers with over double that wounded. It had also cost the Japanese over 1.7 million soldiers. Although these numbers seem very high, they are in fact trivial compared to the estimates of the casualties on both sides if the US invaded the Japanese mainland. At that point, the US had the option of either dropping nuclear weapons or invading the Japanese mainland.
A full invasion of Japan has been estimated to cost Americans 1.7-4 million casualties with the Japanese casualties up in the tens of millions, including nationwide destruction of cities and landscape. Considering that Japanese nation is made up of thousands of different islands (with the vast majority being on the four largest islands) and the Japanese military doctrine including fighting to the death with surrender being a dishonorable option, an invasion was too costly. Dropping the bombs on Hiroshima in Nagasaki should be considered the least costly option, as both cities have made a dramatic recovery over time compared to what an amphibious invasion would have resulted in. Although the atomic bombs were a great tragedy, the other option would have been far worse for both countries.
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