Question

$\sqrt{(2,7....-2,7)/ \frac{7}{9} } + \sqrt{0,444....}$

Answer 1

$\sqrt{\frac{2,7....-2,7}{\frac{7}{9}}}+\sqrt{0.444...}= \\ \\ \sqrt{\frac{\frac{25}{9}-\frac{27}{10}}{\frac{7}{9}}}+\sqrt{\frac{4}{9}}= \\ \\ \sqrt{\frac{\frac{7}{90}}{\frac{7}{9}}}+\frac{2}{3}= \\ \\ \sqrt{\frac{7}{90}.\frac{9}{7}}+\frac{2}{3} = \\ \\ \sqrt{\frac{1}{10}}+\frac{2}{3}= \\ \\ \frac{\sqrt{10}}{10}+\frac{1}{3}=\boxed{\frac{3\sqrt{10}+10}{30}}$

Espero ter ajudado!