Enzalutamide With or Without Radium Ra 223 Dichloride in Patients With Metastatic, Castration-Resistant Prostate Cancer

Inclusion Criteria: * Men with metastatic, castration resistant prostate cancer involving the bone, which is symptomatic or asymptomatic * Castration resistance will be defined as the development of disease progression, defined as one of the following: * Rising PSA x 2 values \>= 2 weeks apart; minimum absolute PSA value 2 ng/mL * Radiographic progression, with at least 1 new site of metastasis * Symptomatic progression (ex: increase in pain despite stable imaging) AND despite ongoing luteinizing hormone-releasing hormone (LHRH) therapy OR testosterone level \< 50 * Men must have osseous metastases, but the presence of visceral metastases will not exclude patients from participation * Prior external beam radiation therapy (\> 4 weeks prior to enrollment) for palliation of osseous metastatic disease is allowed, provided there is at least one osseous metastasis which has not been irradiated and which can be biopsied * No prior docetaxel or cabazitaxel chemotherapy for metastatic castration-resistant prostate cancer (mCRPC) (men treated with prior docetaxel administered as up-front therapy with androgen deprivation therapy \[ADT\] \> 6 months ago will be eligible); prior abiraterone is allowed * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Hemoglobin \>= 9.5 g/dL * Absolute neutrophil count \>= 1,500 * Platelets \>= 100,000 * Total bilirubin within normal institutional limits * Creatinine clearance (calculated or measured) \> 30 mL/min * At le…