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Let's find the 3-adic expansion of sqrt(7)

sqrt(7) = a_0 + 3 a_1 + 9 a_2 + 27 a_3 + ...

7 = 1 mod 3
sqrt(7) = sqrt(1) mod 3
sqrt(7) = 1 mod 3
a_0 = 1

7 = 16 mod 9
sqrt(7) = 4

But we are 3-adic so

sqrt(7) = 1
a_1 = 1

Now mod 27:

7 = 169 mod 27
sqrt(7) = 13 = 1 mod 3
a_2 = 1

etc...