Is there a special name for a field where each number has a square root?

abstract-algebra field-theory terminology

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!


Yes, those fields are called quadratically closed fields.


If you are interested in ordered fields in which every positive element has a square root, then you are looking for Euclidean fields.

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