[tex]a=\sqrt{29-12\sqrt5}-2\sqrt5=\sqrt{20-12\sqrt5+9}-2\sqrt5=\\\\=\sqrt{(2\sqrt5)^2-2*2\sqrt5*3+3^2}-2\sqrt5=\sqrt{(2\sqrt5-3)^2}-2\sqrt5=\\\\=|2\sqrt5-3|-2\sqrt5=2\sqrt5-3-2\sqrt5=-3\in\mathbb{Z}[/tex]
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[tex]a=\sqrt{29-12\sqrt5}-2\sqrt5=\sqrt{20-12\sqrt5+9}-2\sqrt5=\\\\=\sqrt{(2\sqrt5)^2-2*2\sqrt5*3+3^2}-2\sqrt5=\sqrt{(2\sqrt5-3)^2}-2\sqrt5=\\\\=|2\sqrt5-3|-2\sqrt5=2\sqrt5-3-2\sqrt5=-3\in\mathbb{Z}[/tex]