At a canyon training station, Emek and Tara faced three marked platforms above a deep gap. The route instructions said to choose the platform with the smallest positive value. The labels were |3 - sqrt(20)|, sqrt(5)/2, and 9/8. A display beside the first platform showed sqrt(20) as approximately 4, making its value appear to be |3 - 4| = 1. That seemed like the obvious choice, but Tara noticed that the approximation was too rough. They simplified sqrt(20) to 2sqrt(5), so the first value was 2sqrt(5) - 3, approximately 1.472. The second value was approximately 1.118, while 9/8 equaled 1.125. Although the last two values were close, Emek confirmed that sqrt(5)/2 was smaller by comparing their exact forms. They rejected the tempting first route and stepped onto the platform marked sqrt(5)/2. The remaining signals turned green, guiding them safely across the canyon.