If a \(3\) unit perpendicular is used instead of \(1\) unit in the usual square root spiral, what will be the hypotenuse formed from \(\sqrt{n}\)?

Correct answer: \(\sqrt{n+9}\)

The existing hypotenuse is \(\sqrt{n}\), and the new perpendicular side is \(3\) units. By the Pythagorean theorem, the square of the new hypotenuse is \((\sqrt{n})^2+3^2=n+9\). Therefore, the new hypotenuse is \(\sqrt{n+9}\). \(\sqrt{n+3}\) is incorrect because the perpendicular contributes \(3^2=9\), not \(3\). Exam tip: while finding a hypotenuse, add the squares of the two perpendicular sides.