An architect named Rohan is designing a high-tech sustainable park. He uses a specialized number line to mark the positions of various installations. The entrance of the park is treated as the origin (0). Rohan marks the position of a water fountain at a distance that is a rational number, specifically 2.35 units to the right of the entrance. To ensure the aesthetic balance, he needs to place a sculpture at a position represented by an irrational number, √2, which he approximates on the number line using a geometric spiral construction.

During the construction phase, Rohan encounters a problem where he needs to simplify the dimensions of a rectangular garden area. The length of the garden is given by the expression 1 / (√5 – 2) meters. To make the calculation easier for the laborers, he decides to rationalize the denominator. Furthermore, he calculates the total energy consumption of the park’s lighting system, which follows the laws of exponents. The power requirement for one sector is calculated as (5³ × 5⁻¹)¹/² units. Rohan must be extremely precise, as the difference between terminating decimals and non-terminating recurring decimals affects the sensor calibration of the automated irrigation system. He also notes that some measurements result in values like 0.1010010001… which cannot be expressed as a simple fraction, representing the increasing depth of the drainage pipes.