Field extension-Why does this hold?

Question

$K\leq E$ a field extension, $a\in E$ is algebraic over $K$.

Could you explain me why the following holds??

$$K\leq K(a^2)\leq K(a)$$

Answer 1

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

Answer 2

$K\leq K(a^2)$ and $K\leq K(a^2)$ must be clear to you. only thing to see here is that $K(a^2)\leq K(a)$ and if you prove $a^2 \in K(a)$ you are done, right? That is simply closure.