5. k>0: √k,-√k; k<0: i√k,-i√k; k=0:undefined
• Why not ask the students what the graphs of, say, y=x and y=2/x have to do with #3. They might find it interesting how the intersection of a line and a rectangular hyperbola can be used to find the square root of a number!
• Extension to Iteration
Ask students to explore the following iterative formula for square roots:
x1=1 (choose any pos # for initial or start value; I chose 1 as it's an approximation for √2 but any other value is OK!)
x3=(1.5+2/1.5)/2=17/12≈1.417 Note how rapidly we are approaching √2)
[Note: Plug in √2 into the iteration formula (*) to give you a feel for how this works!]