Why were nuclear bomb used in world war 2?

The President didn't want to lose the enormous US casualties, rangeing from 300,000-750,000 depending on various estimates, that were anticipated. Americans are war weary already with 6,000 plus American Casualties from OIF/ OEF. Americans berate the president for the decision today, would you be willing to sacrifice Half a million American Soldiers lives, when you could avoid it. What would you do/?