Odpowiedź:
a) [tex]\sqrt{6}[/tex] * [tex]\sqrt{12}[/tex] = [tex]\sqrt{6*12}[/tex] = [tex]\sqrt{6*6*2}[/tex] =[tex]\sqrt{6^{2}* 2}[/tex] = [tex]6\sqrt{2}[/tex]
b) [tex]\sqrt[3]{6}[/tex] * [tex]\sqrt[3]{9}[/tex] = [tex]\sqrt[3]{6*9}[/tex] = [tex]\sqrt[3]{2*3*3*3}[/tex] = [tex]\sqrt[3]{2*3^{3} }[/tex] = [tex]3\sqrt[2]{2}[/tex]
c) [tex]\sqrt{18} * \sqrt{10} = \sqrt{18 * 10} = \sqrt{9 * 2 * 2 *5} = \sqrt{3^{2} * 2^{2} * 5 } = 3 * 2 *\sqrt{5} = 6\sqrt{5}[/tex]
d) [tex]\sqrt[3]{16} *\sqrt[3]{12} = \sqrt[3]{16 * 12} = \sqrt[3]{ 4 * 4 * 4 * 3} = \sqrt[3]{4^{2} * 3} =4\sqrt[3]{3}[/tex]
e)[tex]\sqrt{35} : \sqrt{28} = \sqrt{35: 28} = \sqrt{\frac{35}{28} } = \sqrt{\frac{7* 5 }{4*7} } = \sqrt{\frac{5}{4} } = \frac{\sqrt{5} }{\sqrt{4} } = \frac{\sqrt{5} }{2}[/tex]
f) [tex]\sqrt[3]{30} : \sqrt[3]{48} = \sqrt[3]{30 : 48} = \sqrt[3]{\frac{30}{48} } = \sqrt[3]{\frac{6*5}{6*8} } = \sqrt[3]{\frac{5}{8} } = \frac{\sqrt[3]{5} }{\sqrt[3]{8} } = \frac{\sqrt[3]{5} }{2}[/tex]
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