when you square this 6+sqrt(2) do you square the six too?

(6 + √2)^2 =

(6 + √2)(6 + √2) =

36 + 12√2 + 2 =

38 + 12√2 

Quite Simply put, yes.

Therefore (6 + √2)²= (36 + 2) = 38

And by the same reasoning

(8 + 6)^2 = 64 + 36 = 100 ?

Rather than  8^2 + (2×8×6) + 6^2 = 64 + 96 + 36 = 196 .