Let
(
R
,
m
)
(R,m)
be a 2-dimensional rational singularity with algebraically closed residue field and for which the associated graded ring is an integrally closed domain. We use the work of Göhner on condition
(
N
)
(N)
and the theory of degree functions developed by Rees and Sharp to give a very short and elementary proof of a formula for the (mixed) multiplicity of complete
m
m
-primary ideals in
(
R
,
m
)
(R,m)
.