Roundup will work fine, it will kill the grass down to the root system and it "supposedly" goes inert once it hits the soil.
If you are looking for a more environmentally friendly product, we use Burn Out, I haven't found it anywhere locally but we order it off of
www.planetnatural.com and it works really well. It's made primarily of vinegar, clove oil and lemon juice. Spraying that stuff on now while it is 100 degrees will immediately get rid of that grass. (I wouldn't spray and rake, I would just spray and leave it alone to do it's thing). Because of the acidity of the spray, just be careful about keeping it away from your eyes, wear sun glasses or something while applying it.