Question

Find three geometric means between 2 and 162.

Answer 1

there's only one geometric mean for the numbers 2 and 162
That's sqrt(2 x 162) = 18

Answer 2

The first geometric mean is 18. The second is sqrt(2 x 18) = 6. The third is sqrt(2 x 6) = 2sqrt(3)

Answer 3

just looking at your question more closely and my answer was not completely correct
the 3 geom. means are 6, 18 and 54 (not 2sqrt3 as cebroski has suggested)
last one is sqrt(18x162)