Take root is an idiom that means to establish oneself firmly in a particular place. There are a number of synonyms for this phrase that can give a similar meaning. One of these synonyms is to become established, which means to settle in a certain place or situation. Another synonym is to put down roots, which means to establish a permanent home or a strong connection. Other synonyms include to take hold, to become rooted, to take hold, to take firm hold, or to become entrenched. All these synonyms suggest an idea of becoming firmly established in a certain place or situation in order to thrive and grow.