[tex]\displaystyle\\1)\\x=\Big[\sqrt{3\cdot0,\!(592)}+\sqrt{30\cdot0,\!0(592)}+\sqrt{300\cdot0,\!00(592)} +\sqrt{3000\cdot0,\!000(392)}\Big]\cdot\frac{3}{4}\\\\\\x=\left[\sqrt{3\cdot\frac{592}{999}}+\sqrt{30\cdot\frac{592}{9990}}+\sqrt{300\cdot\frac{592}{99900}}+\sqrt{3000\cdot\frac{592}{999000}}\right]\cdot\frac{3}{4} \\\\\\x=\left[\sqrt{\frac{592}{333}}+\sqrt{\frac{592}{333}}+\sqrt{\frac{592}{333}}+\sqrt{\frac{592}{333}}\right]\cdot\frac{3}{4}[/tex]
.
[tex]\displaystyle\\x=\left[\sqrt{\frac{37\cdot16}{37\cdot9}}+\sqrt{\frac{37\cdot16}{37\cdot9}}}+\sqrt{\frac{37\cdot16}{37\cdot9}}}+\sqrt{\frac{37\cdot16}{37\cdot9}}}\right]\cdot\frac{3}{4}\\\\\\x=\left[\sqrt{\frac{16}{9}}+\sqrt{\frac{16}{9}}+\sqrt{\frac{16}{9}}+\sqrt{\frac{16}{9}}}\right]\cdot\frac{3}{4}\\\\\\x=\left[\frac{4}{3}+\frac{4}{3}+\frac{4}{3}+\frac{4}{3}}\right]\cdot\frac{3}{4}\\\\\\x=\frac{16}{3}\cdot\frac{3}{4}\\\\x=4=2^2\\\\x=pp\\\\2\in N\subset Q\\\\[/tex]
..
[tex]\displaystyle\\2)\\x=\sqrt{\frac{55}{6,\!(1)}}+\sqrt{\frac{56}{6,\!(2)}}+\sqrt{\frac{57}{6,\!(3)}}+\sqrt{\frac{58}{6,\!(4)}}+\\\\+\sqrt{\frac{59}{6,\!(5)}}+\sqrt{\frac{60}{6,\!(6)}}+\sqrt{\frac{61}{6,\!(7)}}+\sqrt{\frac{62}{6,\!(8)}}[/tex]
.
[tex]\displaystyle\\x=\sqrt{\frac{55}{\dfrac{61-6}{9}}}+\sqrt{\frac{56}{\dfrac{62-6}{9}}}+\sqrt{\frac{57}{\dfrac{63-6}{9}}}+\sqrt{\frac{58}{\dfrac{64-6}{9}}}+\\\\+\sqrt{\frac{59}{\dfrac{65-6}{9}}}+\sqrt{\frac{60}{\dfrac{66-6}{9}}}+\sqrt{\frac{61}{\dfrac{67-6}{9}}}+\sqrt{\frac{62}{\dfrac{68-6}{9}}}}[/tex]
.
[tex]\displaystyle\\x=\sqrt{\frac{55}{\dfrac{55}{9}}}+\sqrt{\frac{56}{\dfrac{56}{9}}}+\sqrt{\frac{57}{\dfrac{57}{9}}}+\sqrt{\frac{58}{\dfrac{58}{9}}}+\sqrt{\frac{59}{\dfrac{59}{9}}}+\sqrt{\frac{60}{\dfrac{60}{9}}}+\sqrt{\frac{61}{\dfrac{61}{9}}}+\sqrt{\frac{62}{\dfrac{62}{9}}}[/tex]
.
[tex]\displaystyle\\x=\sqrt{\frac{55\cdot9}{55}}+\sqrt{\frac{56\cdot9}{56}}+\sqrt{\frac{57\cdot9}{57}}+\sqrt{\frac{58\cdot9}{58}}+\\\\+\sqrt{\frac{59\cdot9}{59}}+\sqrt{\frac{60\cdot9}{60}}+\sqrt{\frac{61\cdot9}{61}}+\sqrt{\frac{62\cdot9}{62}}\\\\\\x=\sqrt{9}+\sqrt{9}+\sqrt{9}+\sqrt{9}+\sqrt{9}+\sqrt{9}+\sqrt{9}+\sqrt{9}\\\\x=3+3+3+3+3+3+3+3\\\\x=8\cdot3\\\\x=24\in N[/tex]
