The words rooted, routed sound the same but have different meanings and spellings. Why do rooted, routed sound the same even though they are completely different words?
The answer is simple: rooted, routed are homophones of the English language.
Fixed in one position; immobile; unable to move.
Ingrained, as through repeated use; entrenched; habitual or instinctive.
Having a basic or fundamental connection (to a thing); based, originating (from).
Having a root.
Simple past tense and past participle of route.
assigned a route
Simple past tense and past participle of rout.
decisively beaten or defeated
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.