Bermuda grass, as its name implies, loves warmer, tropical climates. It grows so thick and strong that it is used for turf on a variety of athletic fields at many different levels of play. However, it is also prone to weeds in large numbers, which can kill the grass, make the yard look overgrown and be uncomfortable to walk on. You can kill weeds in Bermuda grass in a variety of ways.
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Dig them out
By taking a trowel or small shovel, you can simply dig these weeds out of the ground and compost, which should remove them from the yard permanently. It's important to dig out an area around the weed so you are sure to get all of it. This can lead to a number of holes in your hard, which isn't really an improvement from how it looked before, but this is an easy fix. Simply buy another small section of Bermuda grass to patch those holes or carefully take sections of Bermuda from the edges of the yard where it is less noticeable and plant those in the holes. Then reseed those edges of the yard with Bermuda seed. Take the removed weeds as far away from the yard as possible, so there's no chance of them reviving themselves in the grass.
Another convenient way to efficiently remove weeds is to use herbicide with glyphosate, which goes right to the root of the weed and kills it. Common pesticides include Round Up, Touchdown and Vantage, and it's important to purchase the ones that won't kill your lawn along with the weeds, as this will be a counterproductive process. You may want to dig out a small are around the weed or weeds, keep that dirt and grass to the side and then kill the weed with herbicide, isolating it from the rest of the yard. As Bermuda grass is rather durable, once the weed is dead, you should be able to replace the grass you dug up, as long as you've removed the dirt and dead weed with herbicide.
Another option in preventing weeds from coming up in Bermuda grass is to preempt their arrival by regularly spraying the Bermuda lawn with herbicides that keep weeds from growing in the first place. You can apply these herbicides, like MSMA, throughout the spring and early summer to help prevent weeds from growing in the first place. However, keep in mind you're spraying loads of poison on your lawn or field, which may have other unseen consequences later on down the line.