which method do you use to solve this equation.(x-1)^2=7.

Is it the factoring method or the sqare root method

I would take the square root of each side.

(x-1)= +- sqrt7

Now for the factoring method:

(x-1)^2=7
(x-1)^2-7=0
you have a difference of two squares..
((x-1) +sqrt7)((x- 1) -sqrt7)=0

so either term can equal zero. Same answer as above.

Is the answer considered x=1+ or - square root 7 or just root7

The answer to the equation (x-1)^2=7 is x=1+ or - square root 7. So, both values of x, namely x=1+sqrt(7) and x=1-sqrt(7), satisfy the equation.