ABSTRACT
In the previous chapter we saw that constructible numbers can be obtained from the unit segment by addition, subtraction, multiplication, division (the field operations), and by taking square roots of positive numbers. We may, of course, perform any number of these operations in any order we please. Note that being closed under taking square roots of positive elements is a property that K does not share with all fields. For example, 2 ∈ Q (the smallest field of constructible numbers, as we have seen) but
√ 2 /∈ Q.
