[tex]\sqrt{18} =\sqrt{9\cdot 2} =\sqrt{9} \cdot \sqrt{2} =\sqrt{3^{2} } \cdot \sqrt{2} = 3^{2\cdot\frac{1}{2} } \cdot \sqrt{2} =3\sqrt{2} \\\\\\\sqrt{45} =\sqrt{9\cdot 5} =\sqrt{9} \cdot \sqrt{5} =\sqrt{3^{2} } \cdot \sqrt{5} = 3^{2\cdot\frac{1}{2} } \cdot \sqrt{5} =3\sqrt{5} \\\\\\\sqrt{700} =\sqrt{100\cdot 7} =\sqrt{100} \cdot \sqrt{7} =\sqrt{10^{2} } \cdot \sqrt{7} = 10^{2\cdot\frac{1}{2} } \cdot \sqrt{7} =10\sqrt{7} \\\\\\[/tex]
[tex]\sqrt{28} =\sqrt{4\cdot 7} =\sqrt{4} \cdot \sqrt{7} =\sqrt{2^{2} } \cdot \sqrt{7} = 2^{2\cdot\frac{1}{2} } \cdot \sqrt{7} =2\sqrt{7} \\\\\\\sqrt{72} =\sqrt{36\cdot 2} =\sqrt{36} \cdot \sqrt{2} =\sqrt{6^{2} } \cdot \sqrt{2} = 6^{2\cdot\frac{1}{2} } \cdot \sqrt{2} =6\sqrt{2} \\[/tex]
[tex]\sqrt{40} =\sqrt{4\cdot 10} =\sqrt{4} \cdot \sqrt{10} =\sqrt{2^{2} } \cdot \sqrt{10} = 2^{2\cdot\frac{1}{2} } \cdot \sqrt{10} =2\sqrt{10} \\[/tex]
Korzystałam z następujących wzorów:
[tex]\sqrt[n]{x\cdot y} =\sqrt[n]{x} \cdot \sqrt[n]{y} \\\\\sqrt[n]{x^{n} } =x^{n\cdot \frac{1}{n} } =x[/tex]
