[tex]\displaystyle\bf\\\frac{x}{10}=\frac{2+\sqrt{3}}{\sqrt{7+4\sqrt{3}}}\\\\Ne~ocupam~de~radicalul~compus~de~la~numitor\\\\\frac{x}{10}=\frac{2+\sqrt{3}}{\sqrt{7+2\cdot2\cdot\sqrt{3}}} ~~~Observam~ca~2^2+\Big(\sqrt{3}\Big)^2=7\\\\\\\frac{x}{10}=\frac{2+\sqrt{3}}{\sqrt{4+3+2\cdot2\cdot\sqrt{3}}}[/tex]
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[tex]\displaystyle\bf\\\frac{x}{10}=\frac{2+\sqrt{3}}{\sqrt{4+2\cdot2\cdot\sqrt{3}+3}}\\\\\\\frac{x}{10}=\frac{2+\sqrt{3}}{\sqrt{2^2+2\cdot2\cdot\sqrt{3}+\Big(\sqrt{3}\Big)^2}}\\\\\\\frac{x}{10}=\frac{2+\sqrt{3}}{\sqrt{\Big(2+\sqrt{3}\Big)^2}}\\\\\\\frac{x}{10}=\frac{2+\sqrt{3}}{2+\sqrt{3}}\\\\\\\frac{x}{10}=1\\\\\\\implies~~\boxed{\bf x=10}[/tex]
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10 ∈ N si N ⊂ Z ⊂ R
⇒ Orice numar natural este si numar real.
