I did my own benchmarking and my results are contrary to what was said before.

Artemis:~ anakha$ cat temp.rb
require 'benchmark'

n = 413

Benchmark.bmbm(10) do |x|
   x.report("n * n")  { 100000.times { n * n  } }
   x.report("n ** 2") { 100000.times { n ** 2 } }
end
Artemis:~ anakha$ ruby temp.rb
Rehearsal ---------------------------------------------
n * n       0.360000   0.010000   0.370000 (  0.494618)
n ** 2      1.060000   0.020000   1.080000 (  1.425096)
------------------------------------ total: 1.450000sec

                user     system      total        real
n * n       0.350000   0.000000   0.350000 (  0.508331)
n ** 2      1.060000   0.020000   1.080000 (  1.629833)


It shows that n * n is faster.

However this may be an architecture difference. (for reference I'm on
a mac, a G3)