With that kind of explosive power, it would make sense to test each of the three stages separately before stacking them for a mission. But in the 1960s NASA didn't have time to take it slow. That end of decade lunar landing deadline was fast approaching and the Saturn V was the only ticket to get there.
Development on the Saturn V formally began on Jan. 10, 1961, when NASA announced its intention to build what was then called the C-5 rocket. Designed by Wernher von Braun and his German engineering team, it was a followup rocket to the successful Jupiter series. That's how Saturn got its name; it's the next planet after Jupiter.
Things didn't get off to a roaring start. Von Braun took a conservative approach to his rockets. The German way was to build sturdier rockets than were strictly necessary and then test every piece until the kinks were worked out. This philosophy did take its toll on NASA's early efforts. In 1961, von Braun was so concerned about the rate at which his Redstone rocket burned through its fuel he demanded the March 24 test, which was supposed to take Alan Shepard on his first flight, be an additional unmanned test.