take root
take root {v. phr.}
1. To form roots so as to be able to live and grow.
We hope the transplanted apple trees will take root.
2. To be accepted; to be adopted; to live and succeed in a new place.
Many European customs failed to take root in the New World.
The immigrants to our country took root and began to think of themselves as Native Americans.
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Source: A Dictionary of American Idioms