Question

o valor de raiz quadrada de 1,777... dividido por0,111... e

Answer 1

$\sqrt{\frac{1,777...}{0,111...} }= \sqrt{ \frac{1+0,777...}{0,111...}} = \sqrt{ \frac{1+ \frac{7}{9}}{ \frac{1}{9} } }= \sqrt{ \frac{ \frac{9}{9}+ \frac{7}{9}}{ \frac{1}{9} } }= \sqrt{ \frac{ \frac{9+7}{9}}{ \frac{1}{9} } }= \sqrt{ \frac{ \frac{16}{9}}{ \frac{1}{9} } }= \sqrt{ \frac{16}{9} \cdot \frac{9}{1} } \\ = \sqrt{ \frac{144}{9}} = \sqrt{16} =4$