[tex]a = {(1 + \sqrt{3}) }^{2} - \sqrt{12} [/tex]
[tex]a = {1}^{2} + 2 \times 1 \times \sqrt{3} + {( \sqrt{3}) }^{2} - 2 \sqrt{3} [/tex]
[tex]a = 1 + 2 \sqrt{3} + 3 - 2 \sqrt{3} [/tex]
[tex]a = 1 + 3 + 2 \sqrt{3} - 2 \sqrt{3} [/tex]
[tex]a = 4 \: \in \: \mathbb{N}[/tex]
