Hrōþirīks (Proto-Germanic) comes from Proto-Germanic rīks, from Proto-Celtic rīxs, from Proto-Indo-European h₃rḗǵs, from Proto-Indo-European h₃reǵ- — to straighten, to right oneself; right; just.
Ancestry of “Hrōþirīks”, step by step
Hrōþirīks traces back through two separate lines of ancestry.