Question

Seja a=(raiz0,444...+0,555...)sobre 2 e B =0,777... Então calcule o valor de raiz de A + B

Answer 1

Resposta:

Vamos colocar as dízimas em formato de fração:

0,44444.... =4/9

0,555....=5/9

0,7777....=7/9

$a=\frac{\sqrt{0,444...}+0,555...}{2}=\frac{\sqrt{\frac{4}{9}}+\frac{5}{9}}{2}=\frac{\frac{2}{3}+\frac{5}{9}}{2}=\frac{\frac{6+5}{9}}{2}=\frac{\frac{11}{9}}{2}=\frac{11}{9}.\frac{1}{2} =\frac{11}{18}\\\\b=0,77...=\frac{7}{9}\\\\\\\sqrt{a+b}=\sqrt{\frac{11}{18}+\frac{7}{9}}=\sqrt{\frac{11+14}{18}}=\sqrt{\frac{25}{18}}=\frac{5}{\sqrt{18}}=\frac{5}{3\sqrt{2}}=\frac{5}{3}.\frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}=\frac{5}{6}.\sqrt{2}$