1. Вычислите: а) \(\frac{1}{3}\sqrt{324}+20\sqrt{0,36}\); б) \(\sqrt{1,3}\cdot\sqrt{5,2}\); в) \(\frac{\sqrt{28}}{\sqrt{63}}\); г) \(\sqrt{1,1}\cdot\sqrt{9,9}\); д) \(\sqrt{21}\cdot\sqrt{3\frac{6}{7}}\); е) \(15\sqrt{6\frac{2}{3}}\); ж) \(\sqrt{(-2)^6\cdot9,3}\); з) \(\frac{\sqrt{75}}{\sqrt{108}}\); и) \(\frac{\sqrt{147}}{\sqrt{48}}\); к) \(\frac{1}{5}\sqrt{300}-4\sqrt{\frac{3}{16}}-\sqrt{75}\); л) \((3\sqrt2+1)(\sqrt8+2)\); м) \(\frac12\sqrt{200}-7\sqrt{\frac{2}{49}}-\sqrt{72}\); н) \(1-(3\sqrt7+8)(3\sqrt7-8)\).

1. \(\frac13\sqrt{324}+20\sqrt{0,36}=\frac13\cdot18+20\cdot0,6=6+12=18\).
2. \(\sqrt{1,3}\cdot\sqrt{5,2}=\sqrt{1,3\cdot5,2}=\sqrt{6,76}=2,6\).
3. \(\frac{\sqrt{28}}{\sqrt{63}}=\sqrt{\frac{28}{63}}=\sqrt{\frac49}=\frac23\).
4. \(\sqrt{1,1}\cdot\sqrt{9,9}=\sqrt{10,89}=3,3\).
5. \(\sqrt{21}\cdot\sqrt{3\frac67}=\sqrt{21\cdot\frac{27}{7}}=\sqrt{81}=9\).
6. \(15\sqrt{6\frac23}=15\sqrt{\frac{20}{3}}=15\cdot\frac{2\sqrt{15}}3=10\sqrt{15}\).
7. \(\sqrt{(-2)^6\cdot9,3}=\sqrt{64\cdot9,3}=8\sqrt{9,3}\).
8. \(\frac{\sqrt{75}}{\sqrt{108}}=\sqrt{\frac{75}{108}}=\sqrt{\frac{25}{36}}=\frac56\).
9. \(\frac{\sqrt{147}}{\sqrt{48}}=\sqrt{\frac{147}{48}}=\sqrt{\frac{49}{16}}=\frac74\).
10. \(\frac15\sqrt{300}-4\sqrt{\frac3{16}}-\sqrt{75}=2\sqrt3-\sqrt3-5\sqrt3=-4\sqrt3\).
11. \((3\sqrt2+1)(\sqrt8+2)=(3\sqrt2+1)(2\sqrt2+2)=14+8\sqrt2\).
12. \(\frac12\sqrt{200}-7\sqrt{\frac2{49}}-\sqrt{72}=5\sqrt2-\sqrt2-6\sqrt2=-2\sqrt2\).
13. \(1-(3\sqrt7+8)(3\sqrt7-8)=1-((3\sqrt7)^2-8^2)=1-(63-64)=2\).

Ответ: а) 18; б) 2,6; в) \(\frac23\); г) 3,3; д) 9; е) \(10\sqrt{15}\); ж) \(8\sqrt{9,3}\); з) \(\frac56\); и) \(\frac74\); к) \(-4\sqrt3\); л) \(14+8\sqrt2\); м) \(-2\sqrt2\); н) 2.