In square \(ABCD\) shown below, \(\overline{AC}\) is a diagonal and the length of \(\overline{BC}\) is 75 feet. Which of the following quantities is NOT a rational number?

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The triangles in a square are \(45-45-90\) special right triangles with ratios \(1:1:\sqrt{2}\). The diagonal of our square will be \(75\sqrt{2}\), which is an irrational number.