Nutgrass (or nutsedge, its proper name) is indeed a pesky foe! You have a couple of options for controlling it. Although none of them are quick and easy, they will work if you are diligent.
The first option is to rototill and hand dig the nutlets. Each time you till the soil, pick out exposed roots with nutlets. Then wait a few weeks for more to sprout and till again. A second option is to spray the nutsedge with a herbicide containing glyphosate (such as Roundup) if it is in flower beds. Use it at the full labeled strength and wait until the nutsedge is actively growing and has at least 3 to 5 leaves before spraying the patch. Take great care not to get it on desirable plants or they too will be damaged/killed. This will knock the nutsedge back severely. It will return and you should be ready to spray again. After several applications, you will find that the vast majority of the nutsedge is gone.
For lawns choose a product called Manage or Image and follow label directions carefully including watching for which turf grasses you can use it on and during what temperatures you can safely spray.
The key to any approach is to never allow it to reestablish and regain its stored reserves. Keep forcing it to use stored reserves to send up more growth and then quickly dig, rototill or spray it again. If you don't quit you will win!
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