Round up does not sterilize the soil. It does not prevent new grass from being established via seed or sod.

Where do you live?
What kind of grass do you have surrounding the dallis grass?

North Dallas. Bermuda. Last 2 times I mowed I scalped that section of course its not growing back that fast.

With bermuda my unspoken idea won't work. Best left unspoken.

RoundUp is a tough love approach. You have gotten the wrong idea about it from someone. RU kills the grass it gets on. It might take a few days for the grass to show that its dying but it is. Once it is dead, the surviving bermuda surrounding the weeds will be free to fill back in. Typically you can spray RU and the next week plant seed. But if your lawn is a sodded type of bermuda, then don't seed it.

Is this hybrid (i.e. sodded) bermuda or common (seeded) bermuda?

i'm curious ... is your unspoken idea possible for St. Augustine?

gooup, yes, as a matter of fact, it was proved to work on St Augustine. Go to YouTube and search for the video. Use the search words, "baking soda st augustine crabgrass pferrell314." The same idea worked for dallisgrass.