During a mountain orienteering challenge, Emek and Tara reached a sign showing three possible checkpoint coordinates: 3sqrt(2), sqrt(18), and 13/3. Their instructions said to visit the checkpoints from the smallest coordinate value to the largest. The values looked different, and rounding too early could hide an important relationship. Tara simplified sqrt(18) by writing it as sqrt(9 times 2), which gave 3sqrt(2). This showed that two coordinates were exactly equal, even though their original forms looked different. To compare them with 13/3, Emek noted that 3sqrt(2) was about 4.243, while 13/3 was about 4.333. Therefore, the two equivalent radical coordinates came before 13/3. The map marked the equal coordinates as two paths meeting at the same checkpoint, followed by the final trail. Using exact simplification first and approximation only for comparison, Emek and Tara chose the correct route and reached the final camp safely.