If \(OP=\sqrt{73}\) and \(OQ=\sqrt{74}\) are consecutive hypotenuses, what is \(PQ^2\)?

Correct answer: \(1\)

In a square-root spiral, \(OQ\) is the hypotenuse of the next right triangle, while \(OP\) is one of its sides. By Pythagoras' theorem, \(PQ^2=OQ^2-OP^2=74-73=1\). Hence, the correct answer is \(1\). The values \(73\) and \(74\) are \(OP^2\) and \(OQ^2\), respectively, not \(PQ^2\). Exam tip: the difference between the squares of consecutive hypotenuses gives the square of the new perpendicular segment.