The graph shows the curve and the point A. By changing the value in the slider, can you find an approximation for ?

You can see from that graph that , but the answer is not very accurate. The next graph shows the same curve but zoomed in near . Check that the more precise we make the approximation of , becomes more and more accurate. The values of are recorded on the spreadsheet next to the graph.

Since is an irrational number, its decimal expansion does not end, but the software is limited and has to round it at some point. If the software was not a restraint we could get more and more accurate approximations to .

Using the same graph of and knowing that a good approximation for is 1.4142135, can you calculate ?