[tex]zad.1\\\\d)~~~\sqrt{27} \cdot \sqrt{3} =\sqrt{27\cdot 3} =\sqrt{81} =\sqrt{9^{2} } =9\\\\e)~~\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{15} =\sqrt{3\cdot 5\cdot 15} =\sqrt{15\cdot 15}=\sqrt{15^{2} } =15\\\\f)~~\sqrt{2} \cdot \sqrt{8} \cdot \sqrt{10} =\sqrt{2\cdot 8} \cdot \sqrt{10} =\sqrt{16} \cdot \sqrt{10} =\sqrt{4^{2} } \cdot \sqrt{10} =4\sqrt{10}[/tex]
[tex]zad.2\\\\e)~~\dfrac{\sqrt{108} }{\sqrt{3} } =\sqrt{\dfrac{108}{3} } =\sqrt{36} =\sqrt{6^{2} }=6\\\\\\f)~~\dfrac{\sqrt{75} }{\sqrt{25} } =\sqrt{\dfrac{75}{25} } =\sqrt{3} \\\\\\g)~~\dfrac{\sqrt{150} }{\sqrt{6} } =\sqrt{\dfrac{150}{6} } =\sqrt{25} =\sqrt{5^{2} } =5\\\\\\h)~~\dfrac{\sqrt{2} }{\sqrt{32} } =\sqrt{\dfrac{2}{32} } =\sqrt{\dfrac{1}{16} } =\sqrt{\dfrac{1^{2} }{4^{2} } } =\dfrac{1}{4}[/tex]
[tex]zad.3\\\\b)~~\sqrt[3]{3} \cdot \sqrt[3]{9} =\sqrt[3]{3\cdot 9} =\sqrt[3]{27} =\sqrt[3]{3^{3} } =3^{3\cdot \frac{1}{3} } =3\\\\d)~~\sqrt[3]{2} \cdot \sqrt[3]{5} \cdot \sqrt[3]{6} =\sqrt[3]{2\cdot 5\cdot 6} =\sqrt[3]{60} \\[/tex]
[tex]zad.4\\\\b)~~\dfrac{\sqrt[3]{-10} }{\sqrt[3]{2} } =\sqrt[3]{\dfrac{-10}{2} } =\sqrt[3]{-5} \\\\c)~~\dfrac{\sqrt[3]{111} }{\sqrt[3]{111} } =\sqrt[3]{\dfrac{111}{111} } =\sqrt[3]{1} =\sqrt[3]{1^{3} } =1^{3\cdot \frac{1}{3} } =1[/tex]
korzystałam ze wzorów:
[tex]\sqrt[n]{x} \cdot \sqrt[n]{y} =\sqrt[n]{x\cdot y} \\\\\sqrt[n]{x^{n} } =x^{n\cdot \frac{1}{n} } =x\\\\\dfrac{\sqrt[n]{x} }{\sqrt[n]{y} } =\sqrt[n]{\dfrac{x}{y} }[/tex]
