Question

3+2×(raíz quadrada de 2,777...+0,5-0,666...)+1

Answer 1

$2,777...=2+0,777...=2+ \frac{7}{9}= \frac{18}{9} +\frac{7}{9} = \frac{18+7}{9}=\frac{25}{9}\\ \\0,5= \frac{5^{:5}}{10_{:5}}= \frac{1}{2} \\ \\0,666...= \frac{6^{:3}}{9_{:3}}= \frac{2}{3} \\ \\ \\ \\ \ \ \ 3+2\cdot \sqrt{2,777...+0,5-0,666...} +1\\ \\=3+2\cdot \sqrt{\frac{25}{9}+\frac{1}{2}- \frac{2}{3} } +1\\ \\=3+2\cdot \sqrt{\frac{50}{18}+\frac{9}{18}- \frac{12}{18} } +1\\ \\=3+2\cdot \sqrt{\frac{50+9-12}{18}} +1\\ \\=3+2\cdot \sqrt{\frac{47}{18}} +1$