[[Field extension]]
# Quadratic extension

A **quadratic extension** is a [[field extension]] $L : K$ of degree $[L:K] = 2$. #m/def/ring 
Hence $L = K[\sqrt{ d }]$ for some squarefree $d \in K$.
In particular, a quadratic extension of $\mathbb{Q}$ is called a [[Quadratic field]].


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