c)
[tex]\sqrt[3]{54} + \sqrt[3]{128}-\sqrt[3]{432} =\\\\= \sqrt[3]{27\cdot2} + \sqrt[3]{64\cdot2} -\sqrt[3]{216\cdot2} =\\\\=\sqrt[3]{27}\cdot\sqrt[3]{2} + \sqrt[3]{64}\cdot\sqrt[3]{2}-\sqrt[3]{216}\cdot\sqrt[3]{2}=\\\\=\sqrt[3]{3^{3}}\cdot\sqrt[3]{2}+\sqrt[3]{4^{3}}\cdot\sqrt[3]{2} - \sqrt[3]{6^{3}}\cdot\sqrt[3]{2}=\\\\=3\cdot\sqrt[3]{2}+4\cdot\sqrt[3]{2}-6\cdot\sqrt[3]{2}=\\\\=3\sqrt[3]{2}+4\sqrt[3]{2}-6\sqrt[3]{2} =7\sqrt[3]{2}-6\sqrt[3]{2} = \sqrt[3]{2}[/tex]
d)
[tex]\sqrt[3]{2}(\sqrt[3]{500}-\sqrt[3]{4}) = \\\\=\sqrt[3]{2\cdot500} -\sqrt[3]{2\cdot4} =\\\\=\sqrt[3]{1000}-\sqrt[3]{8}=\\\\=\sqrt[3]{10^{3}}-\sqrt[3]{2^{3}} = 10-2 = 8[/tex]
Wyjaśnienie:
[tex]\sqrt[n]{a^{n}\cdot b} = a\sqrt[n]{b}\\\\\sqrt[n]{a}\cdot\sqrt[n]{b} = \sqrt[n]{a\cdot b}[/tex]
