The Brainliest Answer!
First of all I list the basic logarithmic properties to be used in solving the given question:-
1. log_{x}x = 1
2. log_{x} y^{z} = z log_{x} y 

x = log_{0.1}0.001 = log_{0.1} 0.1^{3} = 3
y = log_{9}81 = log_{9} 9^{2} = 2
then,  \sqrt{x-2 \sqrt{y} }  \sqrt{3-2 \sqrt{2} }
we can compare  \sqrt{3-2 \sqrt{2} } as  \sqrt{1+ \sqrt{2} + 2 \sqrt{2}  } =  \sqrt{(1+ \sqrt{2} )^{2} } = 1+ \sqrt{2}

Hence, the value of  \sqrt{x-2 \sqrt{y} } is 1+\sqrt{2}

Please tell me if this is the right answer, or in case of doubt, please comment.
1 5 1
the answer which you gave me was not of the above options but the options given are the right ones actually 4 th step is not clear in the answer plz if you can tell me reply back!!
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Now I see where my mistake is, if you see, I mistakenly compared it to (a+b)^2, so in reality, instead of 1+root2, I should have taken 1- root2 or root2 - 1, so the answer will come as 1 - root2, option c. See... we can compare it to booth (1-root2)^2 or (root2-1)^2. But in order to get desired result, i have taken (1-root2)^2.
Any doubt ? :-)
now it is correct!