For a compositum $k$ of quadratic number fields new explicit units are constructed by taking power-of-two roots of circular units. These units are used to obtain a result concerning the divisibility of the class number of $k$ by a power of $2$.
Radan Kučera. "On the class number of a compositum of real quadratic fields: an approach via circular units." Funct. Approx. Comment. Math. 39 (2) 179 - 189, December 2008. https://doi.org/10.7169/facm/1229696569