Question

square root of 0.4 bar

Answer 1

$\huge\boxed{Answer}$

0.4 bar can be written as 4/9.

root 0.4bar=root (4/9)

=2/3

=0.6 bar (bar only for 6)

$\huge\mathfrak\red{itz\:jyotsana☺}$

Answer 2

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \sqrt{ 0.\bar{4}} }$

EVALUATION

Let us assume that

$\displaystyle \sf{ x = 0.\bar{4} }$

Then

x = 0.4444 . . . . - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 4.4444 . . . . - - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 4

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

$\displaystyle \sf{ \implies \:0. \bar{4}= \frac{4}{9} }$

Now

$\displaystyle \sf{ \sqrt{ 0. \bar{4}} }$

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

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

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

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