[tex]\displaystyle\bf\\n=\sqrt{54\cdot0,(6)}+\sqrt{540\cdot0,0(6)}+\sqrt{5400\cdot0,00(6)}\\\\\\n=\sqrt{54\cdot\frac{6}{9}}+\sqrt{540\cdot\frac{6}{90}}+\sqrt{5400\cdot\frac{6}{900}}\\\\\\n=\sqrt{54\cdot\frac{6}{9}}+\sqrt{540\cdot\frac{6}{90}}+\sqrt{5400\cdot\frac{6}{900}}\\\\\\n=\sqrt{\frac{54\cdot6}{9}}+\sqrt{\frac{540\cdot6}{90}}+\sqrt{\frac{5400\cdot6}{900}}\\\\\\n=\sqrt{\frac{54\cdot6}{9}}+\sqrt{\frac{54\cdot6}{9}}+\sqrt{\frac{54\cdot6}{9}}[/tex]
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[tex]\displaystyle\bf\\n=\sqrt{\frac{6\cdot9\cdot6}{9}}+\sqrt{\frac{6\cdot9\cdot6}{9}}+\sqrt{\frac{6\cdot9\cdot6}{9}}\\\\\\n=\sqrt{\frac{6\cdot9\cdot6}{9}}+\sqrt{\frac{6\cdot9\cdot6}{9}}+\sqrt{\frac{6\cdot9\cdot6}{9}}\\\\\\n=\sqrt{6\cdot6}+\sqrt{6\cdot6}+\sqrt{6\cdot6}\\\\\\n=\sqrt{36}+\sqrt{36}+\sqrt{36}\\\\\\n=6+6+6\\\\\\\boxed{\bf n=18}\\\\Raspuns~corect\!:~~C)~18[/tex]
