You can follow the WordPress docs and leave WordPress in a directory but have it appear to be in root. See http://codex.wordpress.org/Giving_WordPress_Its_Own_Directory#Using_a_pre-existing_subdirectory_install
This will correctly change the location in the database. This might be the best way to go if the host requires WordPress to be in a subfolder for some reason.
Or, you can move all the files to root. See http://codex.wordpress.org/Moving_WordPress This link also includes
recovery information in case you make mistakes in the move.