mettere radici

Literally, “to put roots”.

méttere radici (first-person singular present métto radici, first-person singular past historic mìsi radici, past participle mésso radici, auxiliary avére)

1. (idiomatic) to put down roots
   • 2020, Barack Obama, chapter 24, in Chicca Galli, Paolo Lucca, Giuseppe Maugeri, transl., Una terra promessa [A Promised Land], Garzanti Libri:

     Io credo che questa famiglia vada definita in senso ampio,... che ne facciano parte le famiglie degli immigrati che hanno messo radici e cresciuto i figli qui, anche se non sono entrati dalla porta principale.

     I believed in defining that family broadly—... it included immigrant families that had put down roots and raised kids here, even if they hadn't come through the front door.

     (literally, “I believe this family should be defined broadly,... that immigrants who put down roots and raised their children here are a part of it, even if they did not enter through the front door.”)