Gypsum is hydrated calcium sulfate. a 4.89 g sample of this hydrate was heated, and after the water was driven off, 3.87 g anhydrous calcium sulfate remained. determine the formula of this hydrate and name the compound

You have to find the number of moles of water and calcium sulfate.  
to find the mass of water you subtract 3.87 by 4.89 to get 1.02g water and we are given taht the mass of calcium sulfate is 3.87g
then find the moles of water and calcium sulfate in the sample
1.02/18=0.05667mol water
3.87/136.2=0.0284 mol water
now you have to find how many moles there are per one mole of calcium sufate.
0.05667/0.0284=1.994 which can be rounded to 2 mol water for ever 1 mol calcium sulfate
therefore the formula for this CaSO₄·2H₂O and is called calcium sulfate dihydrate.

I hope this helps