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Quadratic number fields ${\displaystyle \scriptstyle \mathbb {Q} [{\sqrt {d}}]\,}$ are number fields in which all numbers are of the form ${\displaystyle \scriptstyle a+b{\sqrt {d}},\ a,\,b\,\in \,\mathbb {Q} \,}$ and ${\displaystyle \scriptstyle d\,}$ is squarefree.