[tex]zad.6\\\\a)\\\\2\sqrt{5} +6\sqrt{5} =(2+6)\sqrt{5} =8\sqrt{5} \\\\b)\\\\\sqrt{55} \cdot\sqrt{2\frac{1}{5} } =\sqrt{55} \cdot\sqrt{\dfrac{11}{5} } =\sqrt{55\cdot \dfrac{11}{5} } =\sqrt{11\cdot 11} =\sqrt{11^{2} } =11\\\\c)\\\\\sqrt{300} -8\sqrt{3} =\sqrt{100\cdot 3} -8\sqrt{3}=\sqrt{10^{2} \cdot 3} -8\sqrt{3}=10\sqrt{3} -8\sqrt{3}=(10-8)\sqrt{3} =2\sqrt{3}\\\\d)\\\\ 3\sqrt{15}\cdot \dfrac{1}{5} \sqrt{5} =3\cdot \dfrac{1}{5}\sqrt{15\cdot 5} =\dfrac{3}{5}\sqrt{5\cdot 5\cdot 3} =[/tex]
[tex]=\dfrac{3}{5}\sqrt{5^{2} \cdot 3} =\dfrac{3}{5}\cdot 5 \sqrt{3} =3\sqrt{3}\\\\e)\\\\(\dfrac{2\sqrt{6} }{3} )^{2} =\dfrac{2^{2} \cdot (\sqrt{6} )^{2} }{3^{2} } =\dfrac{4\cdot 6}{9} =\dfrac{24}{9} =\dfrac{8}{3}=2\dfrac{2}{3}[/tex]
[tex]zad.7\\\\a)\\\\2\sqrt{13} +5~~<~~13\\\\2\sqrt{13} +5\approx 2\cdot 3,6 +5 \approx 7,2+5\approx 12,2\\\\b)\\\\\frac{\sqrt{30} }{2} -1,5~~> ~~1\\\\\frac{\sqrt{30} }{2} -1,5\approx \frac{5,48 }{2} -1,5\approx 2,74-1,5\approx 1,24\\\\c)\\\\3\sqrt[3]{25} +7~~<~~16\\\\3\sqrt[3]{25} +7\approx 3\cdot 2,92 +7\approx 8,76+7\approx 15\approx 15,76\\\\d)\\\\\dfrac{\sqrt[3]{65} }{2} -1~~>~~0\\\\\dfrac{\sqrt[3]{65} }{2} -1\approx \dfrac{4,02 }{2} -1\approx 2,01-1\approx 1,01[/tex]
