Quadratically closed field

In mathematics, a quadratically closed field is a field in which every element has a square root.
Quadratic closure.
A quadratic closure of a field "F" is a quadratically closed field containing "F" which embeds in any quadratically closed field containing "F". A quadratic closure for any given "F" may be constructed as a subfield of the algebraic closure "F"alg of "F", as the union of all iterated quadratic extensions of "F" in "F"alg.