A cab will be much more expensive. Between 30-35 Euros would be my guess. Taking public transportation would be much cheaper (4.90 Euro) and is perfectly safe. Take the S8 or S9 to Frankfurt main station and then switch to Tram 17 in front of the main building until the station "An der Dammheide". The
website says, that overall this is about a 30 minute ride from station to station. Trains leave the airport every 15 minutes. From the tram station it is a
4-minute walk to the hotel.