Yes, fake. I think your grandmother wore them a lot, though-- if that has any sentimental value for you. I still have my late mother's strand of Majorica imitation pearls, which she wore night and day during the final years of her life.
I'm sorry for your disappointment, but if it's any consolation, pre-owned pearls do not tend to sell for much money unless they have historic value or are a well-known brand like Mikimoto. If you look at "sold" listings of pearls on eBay you will see what I mean; they don't hold their value on resale.
Partly this is because pearl nacre is soft, and wears away over time if the pearls are worn much. (Akoya nacre is quite thin over the bead nucleus -- often no more than a third of a millimeter thick.)
Also, pearls tend to yellow over the years, due to exposure to skin oils, lotions and other cosmetics, etc. and yellowed pearls are not as desirable as white pearls.