TITLE: Is there a special name for a field where each number has a square root?
QUESTION [27 upvotes]: For example, not every number in the field of rational numbers with ordinary addition and multiplication has square root.
Is there a special name for a field where each number has a square root? Can anyone help provide some reference? Thank you!

REPLY [7 votes]: If you are interested in ordered fields in which every positive element has a square root, then you are looking for Euclidean fields.