[tex]\displaystyle\bf\\\Big(3-\sqrt5\Big)^2+\frac{30}{\sqrt{5}} =\\\\=3^2+2\times3\times\Big(-\sqrt5\Big)+\Big(-\sqrt5\Big)^2+\frac{30\times\sqrt{5}}{\Big(\sqrt{5}\Big)\times\Big(\sqrt{5}\Big)}=\\\\=9-6\sqrt5+5+\frac{30\times\sqrt{5}}{5}=\\\\=9-6\sqrt5+5+\frac{6\sqrt{5}}{1}=\\\\=9-6\sqrt5+5+6\sqrt{5}=\\\\=9+5+\underbrace{6\sqrt{5}-6\sqrt{5}}_{=0}=\\\\\\=9+5=\boxed{\bf14\in N}[/tex]
