I might develop a warm up sheet or use graph paper with "smaller" size squares with Areas of 1 unit squared and side lengths of 1. I would have them fill out a similar table of the pattern of smaller squares with the side length of Natural numbers. Then introduce a "bigger" size square with 'EXACTLY' 2 times the Area as per your handout. This might get them to recognize how the side length of  $\sqrt{2}$ can be calculated by deduction.