Yes, it was absolutely necessary for Truman to drop the atomic bomb for the prevention of further casualties and the safety of the U.S. Homeland
Had Truman not dropped the bomb, the war more than likely would have continued for much longer. Truman may have killed more than 400,000 Japanese civilians when the bomb was dropped, but he most likely saved more. He saved thousands of young Americans (Atomic Cafe). The U.S. soldiers would have had to enter the Japanese front and based on the dedication of the average Japanese soldier in the Pacific, the war would have been fought to the last man. Many more U.S. soldiers would have died attempting to end the war on the Japanese