Find the 7-adic distance between -1/3 and the square root of 305 in Q7
My solution is write the 7-adic expansion of -1/3 and square root of 305
the 7-adic expansion of -1/3 := 2 +2*7+2*(7^2)+.... =2.2222222(index 7)
the 7-adic expansion of square root of 305:= 2.2222222(index7) this is one representation of root of 305 but there is another representation of 7-adic expansion
Hence they have the same 7-adic expansion . therefore the distance is 0 in Q7?
Is my attemption right? ( i am not sure whether i caculated these two 7-adic expansion in a right way)