Odpowiedź:
a)
[tex]\sqrt{2} * \sqrt{4\frac{1}{2} } = \sqrt{2} *\sqrt{\frac{9}{2} } = \sqrt{2*\frac{9}{2} } = \sqrt{9} = 3[/tex]
b)
[tex]\sqrt{2\frac{2}{3} } : \sqrt{\frac{2}{3} } = \sqrt{\frac{8}{3} } : \sqrt{\frac{2}{3} } = \sqrt{\frac{8}{3} : \frac{2}{3} } = \sqrt{\frac{8}{3} * \frac{3}{2} } = \sqrt{4} = 2[/tex]
c)
[tex]\sqrt{6,4} : \sqrt{10} = \sqrt{6\frac{4}{10} } : \sqrt{10} = \sqrt{\frac{64}{10} * \frac{1}{10} } = \sqrt{\frac{64}{100} } = \frac{8}{10} = 0.8[/tex]
d)
[tex]\sqrt[3]{10} * \sqrt[3]{0.1} = \sqrt[3]{10 * \frac{1}{10} } = \sqrt[3]{1} = 1[/tex]
e)
[tex]\sqrt[3]{2\frac{2}{3} } * \sqrt[3]{\frac{1}{9} } = \sqrt[3]{\frac{8}{3} } * \sqrt[3]{\frac{1}{9} } = \sqrt[3]{\frac{8}{3} * \frac{1}{9} } = \sqrt[3]{\frac{8}{27} }= \frac{2}{3}[/tex]
f)
[tex]\frac{\sqrt[3]{2.7} }{\sqrt[3]{100} }= \sqrt[3]{2.7 : 100} = \sqrt[3]{2\frac{7}{10} : 100 } = \sqrt[3]{\frac{27}{10} * \frac{1}{100} } = \sqrt[3]{\frac{27}{1000} } = \frac{3}{10} = 0.3[/tex]
g)
[tex]\sqrt[3]{-9} * \sqrt[3]{3} = \sqrt[3]{-9 * 3} = \sqrt[3]{-27} = -3[/tex]
h)
[tex]\frac{\sqrt[3]{128} }{\sqrt[3]{-2} } = \sqrt[3]{128 : (-2)} = \sqrt[3]{-64} = -4[/tex]
i)
[tex]\frac{\sqrt[3]{-0.5} * \sqrt[3]{4} }{\sqrt[3]{16} } = \frac{\sqrt[3]{(-\frac{5}{10}) * 4} }{\sqrt[3]{16} } = \frac{\sqrt[3]{(-\frac{20}{10}) } }{\sqrt[3]{16} } = \frac{\sqrt[3]{-2} }{\sqrt[3]{16} } = \sqrt[3]{-2 : 16} = \sqrt[3]{-\frac{2}{16} } = \sqrt[3]{-\frac{1}{8} } = -\frac{1}{2}[/tex]
