Answer 1

you can use a Taylor series expansion to show that
\[\sqrt{1+\epsilon}\approx1+\frac{\epsilon}{2}\]
So factor out 8 from the sqrt:
\[\sqrt{8} \sqrt{1+\frac{4x}{8}}\]
now use the approximation, and simplify

Answer 2

if x = 0 then wouldn't B be the same as A...?

Answer 3

It is sloppy wording. They mean approximate the square root using a linear function in area where x=0. You have to pick an x where you want the approximation to be reasonably close. Here they picked x at 0, but they want estimates when x is near 0.