Question

Va rog!
Exercițiul 5​

Answer 1

$0,2(6)=\frac{26-2}{90}=\frac{24}{90}=\frac{8}{30}=\frac{4}{15} \\\\1,(3)=\frac{13-1}{9}=\frac{12}{9}=\frac{4}{3} \\\\1,(6)=\frac{16-1}{9}=\frac{15}{9}= \frac{5}{3}\\\\\\1,92=\frac{192}{100}=\frac{48}{25} \\\\(\sqrt{\frac{\frac{4}{15} }{\frac{4}{3} }:\frac{1}{4}} -\frac{1}{3\sqrt{5} } )^3:\sqrt\frac{\frac{5}{3} }{\frac{48}{25} } = (\sqrt{\frac{4}{15} *\frac{3}{4}:\frac{1}{4}}-\frac{1}{3\sqrt{5}})^3: \sqrt{\frac{5}{3}*\frac{25}{48} }$$(\sqrt{\frac{1}{5}*4} - \frac{1}{3\sqrt{5}} )^3:\frac{5\sqrt{5} }{12}= (\sqrt{\frac{4}{5}} - \frac{1}{3\sqrt{5}} )^3:\frac{5\sqrt{5} }{12}\\\\(\frac{2}{\sqrt{5}} - \frac{1}{3\sqrt{5}} )^3:\frac{5\sqrt{5} }{12}= (\frac{6-1}{3\sqrt{5} })^3*\frac{12}{5\sqrt{5} } \\\\(\frac{5}{3\sqrt{5} })^3*\frac{12}{5\sqrt{5} }=\frac{125}{27*5*\sqrt{5} } *\frac{12}{5\sqrt{5} }\\\\\frac{25}{27\sqrt{5} }*\frac{12}{5\sqrt{5} }= \frac{300}{135*5}=\frac{60}{135}=\frac{12}{27}=\frac{4}{9}$