In a square-root spiral, if the new hypotenuse is √(n+1), what was the previous hypotenuse?

Correct answer: √n

The governing concept is the general recurrence rule of a square-root spiral. A perpendicular segment of length 1 unit is erected on the previous hypotenuse. If the previous hypotenuse is √n, the Pythagorean theorem gives the square of the next hypotenuse as (√n)² + 1² = n + 1. Therefore the next hypotenuse is √(n + 1). Reversing this statement, if the new hypotenuse is √(n + 1), the preceding one must be √n. Hence option A is correct. A previous length √(n + 2) would lead to √(n + 3), while √(2n) would generally lead to √(2n + 1). The expression √(n²) is not the preceding spiral term and does not follow the construction rule.