What degree field extensions can we obtain by successively adjoining to a field F a square root of an element of F not a square in F, then square root of some nonsquare in this new field, and so on? Argue from this that a zero of x¹⁴ - 3x² + 12 over Q can never be expressed as a rational function of square roots of rational functions of square roots, and so on, of elements of Q.