Actually, it took three bombs. The two that went off, and the threat of a third (which the U.S. didn't actually have).
The idea that nuclear weapons weren't needed to stop Japan is not historically accurate. Well, sure, Japan would have been forced to through simple attrition, but it would have taken a million allied lives to do it.
Sorry, better them than us. That's war.
I am sorry, but this is simply incorrect and is how the old history books used to teach it. Most of us in our 40s or older were raised and educated with this view of how the war against Japan ended, so I understand why people think this is the truth. But it wasn't until recently that declassified documents from both the US and Japan reveal a slightly different story, and it's a whole lot more complex than just not conducting an invasion of the Japanese home islands, which most certainly would have extended the war by at least a year and cost an estimated million lives of American soldiers, to say nothing of Japanese casualties. That much of the story is true, at least.
The increasing political tensions between Truman, Churchill, and Stalin played a huge part in the decision to drop the bomb. There were also political issues going on internally within the Japanese Empire, with a growing faction recognizing that Japan had no chance to win the war and the only way to save the Japanese culture was to surrender. They, of course, clashed with the hardcore Imperialists who kept insisting that they fight to the last man, woman, and child. All of this was taking place prior to August 6th, unbeknownst to the Allies.
The first bomb was dropped on August 6th. The Soviet Union declared war on Japan and invaded Japanese-occupied territories in China with over a million troops on August 8th. Truman was full aware of the August 8th invasion date, which is why he made the decision to drop the first bomb *before* the Soviet Union declared war. The Japanese decision to surrender was actually made after the Soviet invasion into China began, but the arguments on *how* to surrender kept that decision from being made officially known to the US or USSR. So, the second bomb was dropped on August 9th. It took another week before Hirohito finally stepped in between the arguing factions and made the announcement to surrender. The threat of a third bomb had very little to do with that decision; the timing just happens to be coincidental. Japan would have surrendered even with the threat of a third bomb.
Had the United States chosen to simply blockade the Japanese islands and allow the Soviet Union to drive the Japanese from China, they could have just starved them out, achieving the same result of Japanese surrender without the loss of American lives, *and* without the use of nuclear weapons. But Truman had his new toys that would allow him to bring the war to a very quick end (good for him politically at home) and demonstrate to Stalin the fact that America not only had this new powerful weapon, but was willing to use it in combat. This was meant to keep the Soviet Union in check since both Churchill and Truman already recognized the growing threat to Europe from Stalin. That decision obviously didn't work as intended since the Soviet Union then made developing their own nuclear weapons a priority, and once they did, it was too late to go back, and Cold War 1 began.
All of this information is easily verifiable.
Now, with all that being said, it's easy for me and others to play Monday morning quarterback seven decades later. Truman, Churchill, Stalin, and Hirohito did not have the benefit of knowing how the use of those two weapons would start us down the path that has brought us to where we are today. Had they known how history would play out, I have no doubt that those bombs would not have been dropped and the major powers would have worked together instead of against each other to reshape the post-war world.
However, the fact remains that there was more behind the decision to drop the bomb than the simple story we were taught in school. Yes, not having to invade and saving a million lives was a contributing factor, but it was not the only factor. Actual history is never as simple as history books paint it to be, and everyone here knows that.