Yes, the President would need Congressional approval to “start a war”. However, he does not need Congressional approval to provide immediate defense or to issue an operational decree. For instance, commanding troops to defend Pearl Harbor on Dec 7, 1945 was allowed even though war was not declared until the next day. In current times, Operation Desert Storm or Operation Iraqi Freedom, etc… are good examples. Operation Enduring Freedom (Afghanistan) would not qualify, because Congress voted to go to war against the Taliban in 2001. Iraqi Freedom has been contested since it did in fact turn into a war, but I’m not here to argue that point, just to provide an example for you. I hope this helps. Also, I would cite, but the best citations I found were on wikipedia, which should speak for itself.