Question

Eu preciso que seja bem explicado

Answer 1

Boa noite

$(0,111...) = \frac{1}{9} \Rightarrow\ (0,111...)^{2} = ( \frac{1}{9} )^{2} = \frac{1}{81}$

$(0,333...)= \frac{3}{9} = \frac{1}{3} \Rightarrow\ (0,333...)^{4} = ( \frac{1}{3} )^{4}= \frac{1}{81}$

$0,03= \frac{3}{100}\Rightarrow\ (0,03)^{2} = ( \frac{3}{100} )^{2} = \frac{9}{10000}$

$0,1= \frac{1}{10} \Rightarrow\ (0,1)^{4} = ( \frac{1}{10} )^{4} = \frac{1}{10000}$

Substituindo , temos

$\sqrt{ \frac{ \frac{1}{81} }{ \frac{1}{81} }: \frac{ \frac{9}{10000} }{ \frac{1}{10000} } } = \sqrt{1:9} = \sqrt{ \frac{1}{9} } = \frac{1}{3}$

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