Squared root of periodic tenth...

Algebra Level 2

Solve...

B C A D

Heder Oliveira Dias by Heder Oliveira Dias , 38, Brazil

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3 solutions

0,1111... is 1/9. Then the squared root is 1/3, then the result is 0,3333...

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L e t x = 0.1111 ⋯ \color{#3D99F6}{Let\;x=0.1111\dotsm} 10 x = 1.111 ⋯ \color{#3D99F6}{10x=1.111\dotsm} Subtracting the first equation from the second equation,we get: 10 x − x = 1.1111 ⋯ − 0.11111 ⋯ → 9 x = 1 → x = 1 9 \color{#D61F06}{10x-x=1.1111\dotsm-0.11111\dotsm\rightarrow 9x=1 \rightarrow x=\frac{1}{9}} So the question is 1 9 w h i c h i s 1 3 = 0.333 ⋯ = O p t i o n C \color{#69047E}{\sqrt{\frac{1}{9}} which is \frac{1}{3}=0.333\dotsm=\boxed{Option\;C}}

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Mayank Holmes
Jul 31, 2014

clearly 0.333333...= (1/3) and ((1/3))^2 = 1/9 = 0.111111.......

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