The words radical, radicle sound the same but have different meanings and spellings. Why do radical, radicle sound the same even though they are completely different words?
The answer is simple: radical, radicle are homophones of the English language.
Arising from or going to a root or source; basic: proposed a radical solution to the problem.
Departing markedly from the usual or customary; extreme: radical opinions on education.
Favoring or effecting fundamental or revolutionary changes in current practices, conditions, or institutions: radical political views.
Linguistics Of or being a root: a radical form.
Botany The part of a plant embryo that develops into a root.
Anatomy A small structure, such as a fibril of a nerve, that resembles a root.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").