[tex]zad.1\\a)\\\sqrt{1\frac{13}{36} } =\sqrt{\dfrac{49}{36} } =\sqrt{\dfrac{7^{2} }{6^{2} } } =\dfrac{7}{6}= 1\dfrac{1}{6}\\\\b)\\\sqrt{5^{14} \cdot 5^{8} } =\sqrt{5^{14+8} } =\sqrt{5^{22} } =(5^{22} )^{\frac{1}{2} } =5^{22\cdot \frac{1}{2} } =5^{11} =48~828~125\\\\c)\\\\\sqrt[3]{0,008}=\sqrt[3]{\frac{8}{1000} } =\sqrt[3]{\dfrac{2^{3} }{10^{3} } } =\dfrac{2}{10} =\dfrac{1}{5} \\\\e)\\\\\sqrt{5^{2} -3^{2} } =\sqrt{25-9} =\sqrt{16} =\sqrt{4^{2} } =(4^{2} )^{\frac{1}{2} } =4^{2\cdot \frac{1}{2} } =4[/tex]
[tex]zad.2\\\\a)\\\\\sqrt[3]{54} =\sqrt[3]{27\cdot 2} =\sqrt[3]{3^{3} \cdot 2}=3\sqrt[3]{2} \\\\b)\\\\\sqrt{160} =\sqrt{16\cdot 10} =\sqrt{4^{2} \cdot 10} =4\sqrt{10} \\\\c)\\\\\sqrt[3]{375} =\sqrt[3]{125\cdot 3}=\sqrt[3]{5^{3} \cdot 3}=5\sqrt[3]{3}[/tex]
[tex]zad.3\\\\a)\\\\\dfrac{2}{3} \sqrt{18} =\dfrac{2}{3}\sqrt[2]{18} =\sqrt[2]{\dfrac{2^{2} }{3^{2} } \cdot 18 }=\sqrt[2]{\dfrac{4}{9} \cdot 18 } =\sqrt[2]{8}=\sqrt{8} \\\\\sqrt{8}=\sqrt{4\cdot 2} =\sqrt{2^{2} \cdot 2} =2\sqrt{2} \\\\b)\\\\0,2\sqrt[3]{1000} =\dfrac{2}{10} \sqrt[3]{1000} =\sqrt[3]{\dfrac{2^{3} }{10^{3} } \cdot 1000} =\sqrt[3]{\dfrac{8}{1000 } \cdot 1000} =\sqrt[3]{8} \\\\\sqrt[3]{8}=\sqrt[3]{2^{3} }=2^{2\cdot \frac{1}{2} } =2[/tex]
korzystałam ze wzorów:
[tex]\sqrt[n]{x^{n} } =x^{n\cdot \frac{1}{n} } =x\\\\x\sqrt[n]{y} =\sqrt[n]{x^{n} \cdot y}[/tex]
