Radium Ra 223 Dichloride, Hormone Therapy and Stereotactic Body Radiation Therapy in Treating Patients With Metastatic Prostate Cancer

Inclusion Criteria: * Documented informed consent of participant and/or legally authorized representative * Agreement to provide archival primary or metastatic tumor tissue if available * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Life expectancy \> 12 months * Histologic diagnosis of prostate adenocarcinoma \* Pure small cell carcinoma will be excluded; however, component of neuroendocrine /small cell differentiation will be allowed provided that adenocarcinoma constitutes majority of the tissue specimen * Stage M1 \* Metastatic disease can be documented by bone scan or computed tomography (CT) scan or magnetic resonance imaging (MRI) or positron emission tomography (PET)/CT or the combination of these tests * Up to 4 metastatic lesions: * Must have at least 1 bone lesion AND each non-visceral lesion should be less than 5 cm * Visceral lesions will be limited to one lung lesion (\< 2 cm) or one lymph node; no liver lesions allowed; lymph nodes allowed provided they are not in a field of prior radiation, and if amenable to SBRT (to be reviewed by principal investigator \[PI\]) * Two lesions can be in close proximity (i.e. within 5 cm of each other) if they meet radiation SBRT normal tissue toxicity requirements * If have untreated primary prostate cancer: must undergo debulking prostatectomy * If had prior definitive radiation therapy to the prostate: no evidence of locally persistent or recurrent prostate cancer on digital rectal exam (DRE) and imaging stu…