Used to be, a man could meander into the town hardware store (I think Hinkles (sp?) Hardware in Clarksburg, Ontario) and grab a box of explosives for such tasks. We once (in the 80s) bought a box of forcite 40% for a weekend of fun! Surprised us, how much you actually needed for underground work.
...that might be what you call a twofer (i.e. 2-4-1), you can get rid of the barn too!
A root ball can weigh a LOT. I don't think it takes a very big root ball to equal a cubic yard of dirt (which can be over a ton)
"Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."- Archimedes (paraphrase).
It's surprising what a cable attached 12' (or 16' 20') up the tree can do when your levering out a 3' deep root ball.
I found these numbers on the web (must be true!), but actually the weights seem a little light. These were planting guidelines, not removal, so take them with a grain of salt.
Tree diameter Root Ball Diameter Estimated Weight
1.0 - 1.5" 19" 150 lbs.
1.5 - 2.0" 24" 300 lbs.
2.0 - 2.5" 26" 400 lbs.
2.5 - 3.0" 28" 550 lbs.
3.0 - 3.5" 35" 900 lbs.
3.5 - 4.0" 40" 1,500 lbs.
4.0 - 4.5" 45" 2,200 lbs.
4.5 - 5.0" 51" 3,200 lbs.
5.0 - 6.0" 57" 4,600 lbs.
6.0 - 7.0" 65" 5,500 lbs.