Write an equation that shows the relationship between the side length and the area.

Are any of these numbers a solution to the equation[math]x^2=2[/math]? Explain your reasoning.[br][br][list][*][math]1[/math][/*][*][math]\frac{1}{2}[/math][/*][*][math]\frac{3}{2}[/math][/*][*][math]\frac{7}{5}[/math][/*][/list]

Find some more rational numbers that are close to [math]\sqrt{2}[/math].

Can you find a rational number that is exactly [math]\sqrt{2}[/math]?[br][br]

[size=150]If you have an older calculator evaluate the expression [math](\frac{577}{408})^2[/math] and it will tell you that the answer is 2, which might lead you to think that [math]\sqrt{2}=\frac{577}{408}[/math].[/size][br][br]Explain why you might be suspicious of the calculator’s result.

Find an explanation for why [math]408^2\cdot2[/math] could not possibly equal [math]577^2[/math]. How does this show that [math](\frac{577}{408})^2[/math] could not equal 2?

Repeat these questions for [math](\frac{1414213562375}{10000000000000})^2\ne2[/math]an equation that even many modern calculators and computers will get wrong.