Dig them out...

Or water with Weedol, especially if there are other lawn weeds as well..

Will that really get rid of the roots Stera?

If used properly, it should, though it may take a few applications to get almost all of them.
Good nutrition and management of the lawn will help to keep them from coming back.

There's a good chance it will MG. Digging them out isn't certain either because its so easy to snap the root and then you get multiple plants rather than just one. And digging out a mature one will make quite a big hole in the lawn. Swings and roundabouts really. its also important to make sure you pick all the flowers every day so they don't seed, though they should have about finished flowering now.

Well our dandelions haven't finished flowering yet, neither will they for months! Mind you they are not in a lawn - we don't have such :)

Alas a few of ours have just got their second wind MG - spoke too soon! the main flush seems to be over though.

It seems that we should leave the dandelions to flower as they feed the bees... so just make sure you deadhead them before they become nice wee seed heads :)

Pulling a lawn full of dandelions? Oh, my knees!
Deadheading a lawn full of dandelions? Oh,my knees!!
;)

Mower Tugb?

If dandelions were a bit less cunning, mowing might work. As it is, the plants keep the developing seedhead close to the ground until the night before the seeds are ready to be released. I would have to mow early every morning to catch a significant fraction of them before they flew.

We go out every day and pick all the flowerheads and buds we can see (plus the seedheads that sneaked up on us)but we always miss one or two...
Tug in our damper climate the seedheads are on quite long stalks

Yup seed heads on stalks of several inches... Yes we, or rather at present, Bulba goes round deadheading but you never catch them all! Just remember to put them in your recycling bin not the compost Rjmcrompton

Several inches here, as well, but they grow those several inches within a day or two, and then pop open. As I said, I would have to mow daily to have a hope of catching most of them that way.
Fortunately, dandelions are fairly rare, here in the low desert, but I saw nothing different when I lived among the infested lawns of Flagstaff, Arizona, in the mountains.