Cześć ;-)
Pierwsze cztery przykłady
[tex]a] \ \sqrt{6\cdot6\cdot4\cdot5\cdot5\cdot4}=\sqrt{6^2\cdot4^2\cdot5^2}=\sqrt{6^2}\cdot\sqrt{4^2}\cdot\sqrt{5^2}=6\cdot4\cdot5=120\\\\b] \ \sqrt6\cdot5\sqrt6=5\sqrt{6^2}=5\cdot6=30\\\\c] \ (7\sqrt2-3\sqrt8)\cdot\sqrt2=7\sqrt{2^2}-3\sqrt{8\cdot2}=7\cdot2-3\sqrt{16}=14-3\sqrt{4^2}=\\\\=14-3\cdot4=14-12=2\\\\d] \ \sqrt[3]{54}:\sqrt[3]2=\sqrt[3]{54:2}=\sqrt[3]{27}=\sqrt[3]{3^3}=3[/tex]
Kolejne cztery przykłady
[tex]\sqrt{5\frac{2}{3}}:\sqrt{2\frac{1}{25}}=\sqrt{\frac{17}{3}:\frac{51}{25}}=\sqrt{\frac{\not17^1}{3}\cdot\frac{25}{\not51_3}}=\sqrt{\frac{25}{9}}=\sqrt{\frac{5^2}{3^2}}=\frac{5}{3}=1\frac{2}{3}\\\\\sqrt2\cdot\sqrt{50}=\sqrt{2\cdot50}=\sqrt{100}=\sqrt{10^2}=10\\\\\sqrt[3]{25}:\sqrt[3]{\frac{1}{5}}=\sqrt[3]{25:\frac{1}{5}}=\sqrt[3]{25\cdot5}=\sqrt[3]{5^2\cdot5}=\sqrt[3]{5^3}=5\\\\\sqrt{4\cdot9\cdot16}=\sqrt4\cdot\sqrt9\cdot\sqrt{16}=\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt{4^2}=2\cdot3\cdot4=24[/tex]
Pozdrawiam! ~ JulkaOdMatmy
