Field extension-Why does this hold? $K\leq E$ a field extension, $a\in E$ is algebraic over $K$. 
Could you explain me why the following holds??
$$K\leq K(a^2)\leq K(a)$$

Well by definition $K \leq K(a^2)$.
Then since $a^2 \in K(a)$ ($K(a)$ is closed under multiplication), $K(a^2) \leq K(a)$.
