You don't need a square root formula:

P(3,b+1) and Q(3, b-1) both have the x-coordinate 3 so they are on
the vertical line that passes through x=3 on the x-axis:






To get the idea, first make up a number for b to represent. 
Say b=5

Then  P(3,b+1), Q(3, b-1)

becomes

 P(3,5+1), Q(3, 5-1)

or 

 P(3,6), Q(3,4)

Now plot those two points:



They are two units apart because a line segment drawn between them
is 2 units long, and because if you subtract their y-coordinates, you get
6-4=2

Now choose a different number for b to represent, say b = 1.

Then  P(3,b+1), Q(3, b-1)

becomes

 P(3,2+1), Q(3, 2-1)

or 

 P(3,3), Q(3,1)

Now plot those two points:



They are two units apart because a line segment drawn between them
is 2 units long, and because if you subtract their y-coordinates, you get
3-1=2

Pick other values for b, and you'll always find that 

 P(3,b+1), Q(3, b-1) are always 2 units apart.

That's because their x-coordinate is always 3, so  P(3,b+1) is 
always a point which is two units directly above Q(3, b-1) on that
same vertical line through 3 on the x axis and when you subtract 
their y-coordinates you always get:

(b+1)-(b-1) = b+1-b+1 = b-b+1+1 = 0+2 = 2

And therefore the distance between them will be 2 units no matter 
what number you choose for b to represent.  Choosing b to represent 
different numbers will just cause those two points to "slide" up or 
down that green vertical line, but they will always be 2 units apart.

Edwin