I could actually come up with a real answer if I wanted to. I'll just half-ass it though.

mass of moon ~ 7 x 10^22 kg

In order to completely "blow up" the moon you have to give each piece of the moon enough kinetic energy to send it off to infinity. The escape velocity at the surface of the moon is approximately 2.5 km/s. For simplification I'll neglect the effects of the core of the moon having to be given more energy to escape as it is at the very bottom of the moon's gravitational well. Besides, we don't really need ALL the pieces of the moon to get to infinity before someone would look up to the sky and say "Hey, the moon blowed up!!!"

So we need to set off an explosion which will impart a force on 7 x 10^22 kg sufficient enough to accelerate it to 2.5 km/s. Kinetic energy required is:

1/2 m v^2 = 1/2 * 7 x 10^22 * (2500)^2 = 2.2 x 10^29 J

1 Megaton of TNT = 4.184 x 10^15 J

Therefore, one would need 5.2 x 10^13 megatons of explosive = way way way more than we have. Of course this assumes a lot and is very simplified but it should be within at least a few orders of magnitude.

And there you have a rough answer.