How can I get my mother-in-law with dementia to drink water?

How about ice pops? Small doses of 'milk shakes' --- which can be probiotic yogurt drinks that are flavored, or small amounts of ensure or boost if she can tolerate them and there are no contraindications. Juices?
The memory care where my Mom resided served 2 beverages at each meal and one mid morning and another midafternoon. The staff worked hard to make sure that residents drank all or most of the beverages served. BUT they were served small glasses they could handle and that didn't look overwhelming. I find with my MIL that if I just put a small amount in a glass,she does better than giving her a full glass.

fregflyer thanks We will try the watermelon BC she will eat it and does like some ice cream

Does Mom like watermelon? If yes, give her a plate full, that fruit contains a lot of liquid. Same with soups, add some water to it, just don't let her see you do that. What about ice cream?

We try but she might drink a small 6oz root beer once a day but that"s it.

SoninlawBill66, like cwillie mentioned above, your mother-in-law can drink something else, as long as she gets enough liquid into her system.

So give her something else she likes better.