Zadanie 1
a)
\frac{2\sqrt2}{\sqrt3-1}=\frac{2\sqrt2(\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)}=\frac{2\sqrt2(\sqrt3+1)}{3-1}=\frac{2\sqrt2(\sqrt3+1)}{2}=\sqrt2(\sqrt3+1)=\sqrt6+\sqrt2
b)
\frac{2\sqrt3}{3\sqrt5}=\frac{2\sqrt3*\sqrt5}{3\sqrt5*\sqrt5}=\frac{2\sqrt{15}}{3*5}=\frac{2\sqrt{15}}{15}
Zadanie 2
a)
(3\sqrt2+1)(3\sqrt2-1)=(3\sqrt2)^2-1^2=9*2-1=17
b)
\frac{4^{-\frac{2}{3}}*12^{\frac{2}{3}}}{6^{\frac{1}{3}}*4^{-\frac{2}{3}}}=\frac{12^{\frac{2}{3}}}{6^{\frac{1}{3}}}=\frac{6^{\frac{2}{3}}*2^{\frac{2}{3}}}{6^{\frac{1}{3}}}=6^{\frac{2}{3}-\frac{1}{3}}*2^{\frac{2}{3}}=6^{\frac{1}{3}}*2^{\frac{2}{3}}=\sqrt[3]6*\sqrt[3]{2^2}=\sqrt[3]{6*4}=\sqrt[3]{24}=\sqrt[3]{8*3}=2\sqrt[3]3