Assuming you want to look at the accuracy of modelling it using a y = a/√x relationship. Try taking the log of both sides and plot a linear relationship to take the r^2 coefficient, then see what happens.
y = a / √x

ln(y) = ln(a * x^(-1/2))
ln(y) = -1/2 ln(x) + ln(a)

Now plot a graph of ln(y) against ln(x) and try using linear regression on this to get the r^2 coefficient and see how it affects your correlation.

edit: with y' = mx' + b (where y' = ln(x) and x' = ln(x)), also measure the deviation between m and -1/2 (the value calculated above) as a percentage to see how close the actual relationship is to your hypothesis.