Prepare the tapioca pearls. Bring to a boil 6 cups of water, and then add in the tapioca pearls and a hint of sugar. Cook for 4 minutes, until they are all floating. then drain them and set aside.
Prepare the honeydew smoothie. Blend the frozen honeydew chunks with the coconut water, cucumber, and mint in a high speed blender until smooth.
Serve. Divide the tapioca pearls among 3 large glasses, and then divide the honeydew smothie among the three glasses. Yum!