British spelling of 'familiarize'; to make something familiar to someone, or to become well acquainted with something through repeated experience.
From Latin 'familiāris' (familiar, intimate) plus the suffix '-ise' (British English standard verb ending), versus American '-ize.' The root 'familia' means household.
British English uses '-ise' endings while American English uses '-ize,' a split that happened centuries ago—'familiarise' itself shows how the same root word evolved differently across the Atlantic!
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