Question

√0.444... [Square root of 0.444...]

Answer 1

Answer:

If the bar is on 4 then √0.4...=0.6...

Here bar will be on 6

For clearification, I have pined the answer image, you can check it

If it's √0.444 then it will be equal to 0.6663332 or 0.6663 or 0.66(It's enough to take till 2 digit of decimal place) so take 0.66

Hope you may get it

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Answer 2

SOLUTION

TO DETERMINE

$\sf{ \sqrt{0.444...} }$

EVALUATION

Let x = 0.444 . . . . - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 4.444 . . . . - - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 4

$\displaystyle \sf{ \implies x = \frac{4}{9} }$

$\displaystyle \sf{ \implies 0.444... = \frac{4}{9} }$

Now

$\displaystyle \sf{ \sqrt{0.444... }}$

$\displaystyle \sf{ = \sqrt{ \frac{4}{9} }}$

$\displaystyle \sf{ = \frac{ \sqrt{4} }{ \sqrt{9} } }$

$\displaystyle \sf{ = \frac{2 }{ 3 } }$

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