[tex]Zastosowano\ \ wlasno\'sci\ \ pierwiastk\'ow\\\\\sqrt{a^2}=a\\\\(\sqrt{a})^2=a\\\\(\sqrt[3]{a})^3=a\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}} \\\\\\a)\ \ (\sqrt[3]{7})^3+(\sqrt{11})^2=7+11=18\\\\b)\ \ (\sqrt{23})^2-\sqrt[3]{13^3}=23-13=10\\\\c)\ \ (\sqrt[3]{4})^3+(\sqrt{5})^2=4+5=9\\\\d)\ \ (3\sqrt{7})^2-(2\sqrt[3]{5})^3=3^2\cdot(\sqrt{7})^2-2^3\cdot(\sqrt[3]{5})^3=9\cdot7-8\cdot5=63-40=23\\\\e)\ \ 4(\sqrt[3]{10})^2+(2\sqrt{3})^2=4\cdot\sqrt[3]{100}+2^2\cdot(\sqrt{3})^2=4\sqrt[3]{100}+4\cdot3=4\sqrt[3]{100}+12[/tex]
przykład e) chyba błędnie zapisany jeśli będzie taki zapis
[tex]e)\ \ 4(\sqrt[3]{10})^3+(2\sqrt{3})^2=4\cdot10+2^2\cdot(\sqrt{3})^2=40+4\cdot3=40+12=52\\\\f)\ \ (\sqrt[3]{5})^6-(\sqrt{2})^6=(5^{\frac{1}{3}})^6-2^{\frac{6}{2}}=5^{\frac{6}{3}}-2^3=5^2-2^3=25-8=17[/tex]
