rooting / routing are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
rooting: (noun) the process of putting forth roots and beginning to grow.
routing: (verb) send documents or materials to appropriate destinations. (verb) send via a specific route. (verb) divert in a specified direction.
rooting: r·UW·t·ih·ng
routing: r·AW·t·ih·ng
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)