In these type of questions where master method doesnt apply you can do the following
$T(n) = 2T(n/4) + \sqrt{3}$
Reframe it like this, by putting i in the specified positions
$T(n) = 2^{i}T(n/4^{i}) + i\sqrt{3}$
Now for n/4i = 1, put i = log4n
So the equation becomes
$T(n) = 2^{log_{4}n} + log_{4}n\sqrt{3}$
Or
$T(n) = n^{log_{4}2} + log_{4}n\sqrt{3}$
$T(n) = \sqrt{n} + log_{4}n\sqrt{3}$
And therefore
$T(n) = O(\sqrt{n})$