Question

Determine o valor da expressão

expressão na imagem​

Answer 1

$\sqrt{1,7777...}=\sqrt{x}\therefore 1,7777...=x \implies 17,7777...=10x \\\therefore 10x-x=9x=17,777...-1,777...=17-1=16\therefore 9x=16\therefore x=\frac{16}{9}\\\sqrt{x}=\sqrt{\frac{16}{9}}=\frac{4}{3}\\\\7,666...=y\implies 76,666...=10y\therefore 10y-y=9y=76,666...-7,666...\\\\\therefore 9y=69\therefore y=\frac{69}{9}=\frac{23}{3}\\\\\sqrt{x}+y=\frac{4}{3}+\frac{23}{3}=\frac{27}{3}=\boxed{9}$