  We give effective proofs of residual finiteness and conjugacy separability
for finitely generated nilpotent groups. In particular, we give precise
asymptotic bounds for a function introduced by Bou-Rabee that measures how
large the quotients that are need to separate non-identity elements of bounded
length from the identity which improves the work of Bou-Rabee. Similarly, we
give polynomial upper and lower bounds for an analogous function introduced by
Lawton, Louder, and McReynolds that measures how large the quotients that are
need to separate pairs of distinct conjugacy classes of bounded work length
using work Blackburn and Mal'tsev.
