Ask Mr. Smarty Plants

You aren't going to like this, but in both cases simply pulling it out again and again and again is the time-honored method. An organic approach, which we have never tried, is found in Gardens Alive Is Nutgrass Driving You Nuts? The problem, even with very intense organic or chemical pesticides, is that the rhizomes, deep underground, will hold nourishment for the plant for a very long time, usually permitting it to overcome attempts to do it in. If you pull off the leaves of a plant long enough, the roots will finally starve, because there are no leaves making food for the whole plant through photosynthesis.  If your ground is soft, there is no greater satisfaction than pulling out a long string of those tubers and destroying them. Unfortunately, there are always more a few feet away, and they will quickly grow into the vacated space. Cyperus rotundus is native to Africa, south central Europe and southern Asia. If we could deport it, we would. 

Pictures of Cyperus rotundus from Google

From our webpage on  Fragaria virginiana (Virginia strawberry):

"Virginia strawberry or wild strawberry is a ground-hugging plant rising from a fibrous, perennial root system. Hairy leaf petioles, up to 6 in. long, each bear a single trifoliate leaf. The hairy flower stalk gives rise to a loose cluster of small, five-petaled flowers followed by tasty, wild strawberries."

This means you have a similar problem to the nutgrass, in that the underground roots are perennial, and will live in the soil to send fresh new plants up. From Illinois Wildflowers, we learned that it is  considered a food plant, as well as a host to butterflies and other wildlife. No one seems too interested in getting rid of it. When you read about it, you realize it is much the same situation as the nutgrass, spreading by stolons and rhizomes. However, it apparently goes dormant in warm weather; that might be a good time to launch an attack. Or try making strawberry jam.

From our Native Plant Image Gallery:

Fragaria virginiana

Fragaria virginiana

Fragaria virginiana