Other forms: rootlessly
Someone who's rootless doesn't have a permanent home or place to settle down. Your rootless cousin might save money for a ticket to India and then spend years backpacking around Asia.
Some plants are literally rootless, growing without a root system to absorb nutrients. Algae is one example of a rootless plant. Rootless far more commonly describes a person who wanders. An immigrant might feel a bit rootless the first few years in a new country, not quite at home yet but far from their original home. And if your family moves every couple of years, they're rootless too.