This phase 2 trial studies radium Ra 223 dichloride, hormone therapy and stereotactic body radiation in treating patients with prostate cancer that has spread to other places in the body. Radium Ra 223 dichloride contains a radioactive substance that collects in the bone and gives off radiation that may kill cancer cells. Hormone therapy using leuprolide acetate or goserelin acetate may fight prostate cancer by lowering the amount of testosterone the body makes. Stereotactic body radiation therapy is a specialized radiation therapy that sends x-rays directly to the tumor using smaller doses over several days and may cause less damage to normal tissue. Giving radium Ra 223 dichloride, hormone therapy and stereotactic body radiation may work better at treating prostate cancer.