In a square root spiral, which hypotenuse is formed after \(\sqrt{1023}\), and what is its exact value?

Correct answer: \(\sqrt{1024}=32\)

In a square root spiral, successive hypotenuses are \(\sqrt{1}, \sqrt{2}, \sqrt{3}\), and so on. Hence, the hypotenuse after \(\sqrt{1023}\) is \(\sqrt{1024}\). Since \(1024=32^2\), \(\sqrt{1024}=32\). \(\sqrt{1025}\) is the following hypotenuse, not the immediate next one. Exam tip: remember nearby perfect squares; \(32^2=1024\).