Is it possible to prove directly that even perfect squares have even square roots? Or, symbolically:

$\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$ $\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$

$\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$ $\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$