Nice, but I think that it can be simplified further.
sqrt(a) - sqrt(b) = sqrt(8-4sqrt(3))
a + b - 2sqrt(ab) = 8 - 4sqrt(3)
a + b = 8
ab = 12
a = 6, b = 2. *Note that a > b because sqrt(8-4sqrt(3)) is positive.
sqrt(6) - sqrt(2) = sqrt(8-4sqrt(3))
=^._.^=
+179 
