19. \(\sqrt{a^2 + 10ab + 25b^2}\) при \(a = \frac{7}{11}\) и \(b = \frac{3}{11}\)

\(\sqrt{a^2 + 10ab + 25b^2} = \sqrt{(a + 5b)^2} = |a + 5b|\)
Подставляем \(a = \frac{7}{11}\) и \(b = \frac{3}{11}\): \(|\frac{7}{11} + 5 \cdot \frac{3}{11}| = |\frac{7}{11} + \frac{15}{11}| = |\frac{22}{11}| = 2\)
Ответ: 2