##sqrt(2)/6##
It is a matter of splitting the numbers up into factors that have a root if you can. Then taking these outside of the root by applying that root.
What factors are there of 8 that we can apply a root to? The obvious ones are 2 and 9 as ##2 times 9 =18## we can take the root of 9 but not of 2. So we end up with:
##sqrt((1/18)) = sqrt(1/(2 times 9)##
This can be split so that we have:
##sqrt(1/2 times 1/9) = 1/3 sqrt(1/2)##
But convention is that you do not have a root as a denominator if you can help it.
Write as: ##1/3 (sqrt(1))/( sqrt(2))## This does work. Check it on a calculator.
But ##sqrt(1) =1## giving:
##1/3 times 1/(sqrt(2))##
To ‘get rid’ of the root in the denominator multiply by the value 1 (does not change the overall values) but write the 1 in the form of ##(sqrt(2))/(sqrt(2))## giving:
##1/3 times 1/sqrt(2) times sqrt(2)/sqrt(2)##
But ##sqrt(2) times sqrt(2) = 2##
So now we have: ##1/3 sqrt(2)/2 = sqrt(2)/6##
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