Is this an over-the-air update, or did you update while being connected to a computer?
iOS 8.2 and above take up around 2 GB more space, which requires that you have more space on your device. If you tried the over-the-air update (updating directly form the iPad in Settings>General>Update) this issue could be resolved by updating through a computer with iTunes installed on it. Updating through a computer requires less space on the device, because it pulls the SW out before replacing it, while over-the-air updates install the new SW before removing the old one.
If this doesn't work, or you in general want to know how you can manage your storage better, try managing storage through Settings>Usage>Storage>Manage storage. This function allows you to view what is taking up storage, and it allows you to more easily remove data you do not wish to keep on the device.
Good luck.