Задание 4. Найдите значение выражения: 1. \(\sqrt{a^2+8ab+16b^2}\) при \(a=3\frac{3}{7}, b=\frac{1}{7}\); 2. \(\sqrt{a^2+12ab+36b^2}\) при \(a=7\frac{2}{5}, b=\frac{3}{5}\); 3. \(\sqrt{a^2+10ab+25b^2}\) при \(a=1\frac{6}{13}, b=\frac{4}{13}\); 4. \(\sqrt{a^2+8ab+16b^2}\) при \(a=3\frac{2}{3}, b=\frac{1}{3}\); 5. \(\sqrt{9a^2+6ab+b^2}\) при \(a=\frac{5}{13}, b=6\frac{11}{13}\); 6. \(\sqrt{16a^2+8ab+b^2}\) при \(a=\frac{3}{11}, b=5\frac{10}{11}\); 7. \(\sqrt{25a^2+10ab+b^2}\) при \(a=\frac{4}{9}, b=3\frac{7}{9}\); 8. \(\sqrt{36a^2+12ab+b^2}\) при \(a=\frac{4}{5}, b=8\frac{1}{5}\); 9. \(\sqrt{a^2-6ab+9b^2}\) при \(a=3, b=6\); 10. \(\sqrt{a^2-12ab+36b^2}\) при \(a=8, b=3\); 11. \(\sqrt{a^2-8ab+16b^2}\) при \(a=4, b=3\); 12. \(\sqrt{a^2-10ab+25b^2}\) при \(a=7, b=2\); 13. \(\sqrt{a^2+10ab+25b^2}\) при \(a=8, b=-2\); 14. \(\sqrt{a^2+6ab+9b^2}\) при \(a=5, b=-4\); 15. \(\sqrt{a^2+12ab+36b^2}\) при \(a=7, b=-3\); 16. \(\sqrt{a^2+4ab+4b^2}\) при \(a=2, b=-4\).

Задание 4. Найдите значение выражения: 1. \(\sqrt{a^2+8ab+16b^2} = \sqrt{(a+4b)^2} = |a+4b|\) * \(a=3\frac{3}{7}=\frac{24}{7}, b=\frac{1}{7}\) * \(|\frac{24}{7}+4\cdot\frac{1}{7}| = |\frac{24}{7}+\frac{4}{7}| = |\frac{28}{7}| = |4| = 4\). 2. \(\sqrt{a^2+12ab+36b^2} = \sqrt{(a+6b)^2} = |a+6b|\) * \(a=7\frac{2}{5}=\frac{37}{5}, b=\frac{3}{5}\) * \(|\frac{37}{5}+6\cdot\frac{3}{5}| = |\frac{37}{5}+\frac{18}{5}| = |\frac{55}{5}| = |11| = 11\). 3. \(\sqrt{a^2+10ab+25b^2} = \sqrt{(a+5b)^2} = |a+5b|\) * \(a=1\frac{6}{13}=\frac{19}{13}, b=\frac{4}{13}\) * \(|\frac{19}{13}+5\cdot\frac{4}{13}| = |\frac{19}{13}+\frac{20}{13}| = |\frac{39}{13}| = |3| = 3\). 4. \(\sqrt{a^2+8ab+16b^2} = \sqrt{(a+4b)^2} = |a+4b|\) * \(a=3\frac{2}{3}=\frac{11}{3}, b=\frac{1}{3}\) * \(|\frac{11}{3}+4\cdot\frac{1}{3}| = |\frac{11}{3}+\frac{4}{3}| = |\frac{15}{3}| = |5| = 5\). 5. \(\sqrt{9a^2+6ab+b^2} = \sqrt{(3a+b)^2} = |3a+b|\) * \(a=\frac{5}{13}, b=6\frac{11}{13}=\frac{89}{13}\) * \(|3\cdot\frac{5}{13}+\frac{89}{13}| = |\frac{15}{13}+\frac{89}{13}| = |\frac{104}{13}| = |8| = 8\). 6. \(\sqrt{16a^2+8ab+b^2} = \sqrt{(4a+b)^2} = |4a+b|\) * \(a=\frac{3}{11}, b=5\frac{10}{11}=\frac{65}{11}\) * \(|4\cdot\frac{3}{11}+\frac{65}{11}| = |\frac{12}{11}+\frac{65}{11}| = |\frac{77}{11}| = |7| = 7\). 7. \(\sqrt{25a^2+10ab+b^2} = \sqrt{(5a+b)^2} = |5a+b|\) * \(a=\frac{4}{9}, b=3\frac{7}{9}=\frac{34}{9}\) * \(|5\cdot\frac{4}{9}+\frac{34}{9}| = |\frac{20}{9}+\frac{34}{9}| = |\frac{54}{9}| = |6| = 6\). 8. \(\sqrt{36a^2+12ab+b^2} = \sqrt{(6a+b)^2} = |6a+b|\) * \(a=\frac{4}{5}, b=8\frac{1}{5}=\frac{41}{5}\) * \(|6\cdot\frac{4}{5}+\frac{41}{5}| = |\frac{24}{5}+\frac{41}{5}| = |\frac{65}{5}| = |13| = 13\). 9. \(\sqrt{a^2-6ab+9b^2} = \sqrt{(a-3b)^2} = |a-3b|\) * \(a=3, b=6\) * \(|3-3\cdot6| = |3-18| = |-15| = 15\). 10. \(\sqrt{a^2-12ab+36b^2} = \sqrt{(a-6b)^2} = |a-6b|\) * \(a=8, b=3\) * \(|8-6\cdot3| = |8-18| = |-10| = 10\). 11. \(\sqrt{a^2-8ab+16b^2} = \sqrt{(a-4b)^2} = |a-4b|\) * \(a=4, b=3\) * \(|4-4\cdot3| = |4-12| = |-8| = 8\). 12. \(\sqrt{a^2-10ab+25b^2} = \sqrt{(a-5b)^2} = |a-5b|\) * \(a=7, b=2\) * \(|7-5\cdot2| = |7-10| = |-3| = 3\). 13. \(\sqrt{a^2+10ab+25b^2} = \sqrt{(a+5b)^2} = |a+5b|\) * \(a=8, b=-2\) * \(|8+5\cdot(-2)| = |8-10| = |-2| = 2\). 14. \(\sqrt{a^2+6ab+9b^2} = \sqrt{(a+3b)^2} = |a+3b|\) * \(a=5, b=-4\) * \(|5+3\cdot(-4)| = |5-12| = |-7| = 7\). 15. \(\sqrt{a^2+12ab+36b^2} = \sqrt{(a+6b)^2} = |a+6b|\) * \(a=7, b=-3\) * \(|7+6\cdot(-3)| = |7-18| = |-11| = 11\). 16. \(\sqrt{a^2+4ab+4b^2} = \sqrt{(a+2b)^2} = |a+2b|\) * \(a=2, b=-4\) * \(|2+2\cdot(-4)| = |2-8| = |-6| = 6\).