Yes, you can easily trap them out of acreage that size.
This is the ONE animal that I have become pretty good at trapping. I have tried many methods but I will share what has worked for me. First, I had to find the right trap. I tried different kinds, but the Macabee style works best and is easiest. I would suggest getting 6-8 of them. You can get them at hardware or farm supply stores, got mine at TSC.
There are you tube videos out there to show you how to set them. Forget about the videos and instructions that have you excavating soil to catch these critters. Keep it simple, takes a few minutes. Find the freshest hole, look for evidence of fresh dirt. The dirt will be in a fan shape, many times you can see a small round pile in the middle of the inside of the arc, this is the hole. If you can't see it, probe around with something. The tunnel will generally be in the direction opposite the fan shape of the mound.
Use a hand held garden trowel/spade to dig the loose dirt out of the hole, keep digging until you feel it break through, you want it good and open. The gophers don't like air in their tunnel and will come try to plug it, setting off the trap. Make the hole big enough for your trap and shove it as far down as you can, I like to leave it just enough where I can still see the trip pan. Done. Don't cover the hole. I don't use bait, and I don't worry about human scent.
1. Tie something to your trap. I usually set 2 as there is always more than one hole. I tie them together with a thin tie out cable for a dog so I don't stake them down. (I did have a coyote run off with my two traps once)
2. Knock down all the mounds near your traps so you know if a fresh one shows up. I have had them avoid the trap and dig a new hole. Just set the new hole and you'll get him.
3. You will have them bury your trap once in a while. No big deal just reset, still beats excavating new holes and covering like some instructions say.
4. Only set fresh holes.
5. I leave a little loose dirt in the bottom of the tunnel so when I set my trap I rub it back and forth so the trap is slightly bedded. Seems if they walk on dirt rather than the trap I have less trouble with burying.
6. Once the trap is in the hole, pull back on the trip pan to give it a "hair trigger", you will see what I mean when you set the trap.
7. Keep after them! Watch for fresh mounds nearby, trap them out around the perimeter as they show up.