 This pilot clinical trial studies combined fluorine F 18 sodium fluoride NaF fludeoxyglucose F 18 FDG positron emission tomography PET and magnetic resonance imaging MRI in measuring response to a drug, radium Ra 223 dichloride Ra-223, in treating patients with prostate cancer that has not responded to hormone therapy and has spread to other parts of the body. Combining NaFFDG in a simultaneous PETMRI scan may help doctors accurately measure how well patients respond to treatment with radium Ra 223 dichloride. 