Smooth is both an adjective and a verb. If you want to make something smooth, you smooth it. Smoothen, a verb meaning to make or become smooth, is listed in a few dictionaries but is superfluous. It always bears replacement with smooth.
Smoothe, which appears about a tenth as often as smoothen, is not a dictionary-recognized word, but we can understand why people might be tempted to use it. Consider the nouns breath, teeth, and sheath. Each has a corresponding verb ending in e—breathe, teethe, and sheathe. Yet while these nouns are pronounced differently from their verbs—the nouns with a hard th, the verbs with a soft one—smooth and its verb are pronounced the same. (Of course, since smooth is pronounced with a soft th, it would be logical for both the noun and the verb to be spelled smoothe. English is weird sometimes.)
Examples
In each of these sentences, smoothe or smoothen could be replaced with smooth:
Impress Skin Care is a skincare routine with clinically proven ingredients to lift, tighten, smoothe, coloration & brighten skin. [AZ Family]
Blue Line trains will share a track between Stadium-Armory and Addison Road-Seat Pleasant while repairs are made to slabs under the rails to smoothen the ride. [Washington Post]
He and Mr Maroni met last week to smoothe over their row over the handling of migrants … [The Economist]
… long-term investors should make only a small allocation, of 5% or less, to oil or oil-related securities as a way to smoothen volatility in their portfolios. [Wall Street Journal]
Although here we’ve used examples from American and British publications, smoothen appears most often in Indian English. We don’t know why this is.
