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## Homework Statement

Show that the field C of constructible numbers is the smallest subfield of R with the property that [tex]a\in C, a>0 \Rightarrow \sqrt{a}\in C[/tex].

## The Attempt at a Solution

Suppose there's a proper subfield of C' of C that has that property, then let [tex]a\in C-C'[/tex]. Somehow I must show that a is actually in C. Perhaps repeated squaring?