val

The root val comes from Latin valēre, a verb with a wonderfully wide reach. At its core it meant "to be strong, to be well, to be worth." A healthy Roman soldier valēbat — he was fit and powerful. A coin valēbat — it was worth a certain amount. The same word covered physical strength, good health, and monetary worth, because to a Roman these were all forms of the same thing: having power, holding up, counting for something.

From the "worth" side of valēre English built its biggest val family — the value cluster:

- value = the worth of something
- valuable = having a lot of worth
- invaluable = so valuable its worth can't even be measured (the in- here means "not [measurable]," not "worthless")
- evaluate = e- (out) + value → to draw the worth out, to judge how much something is worth
- devalue / undervalue / overvalue = to push worth down, set it too low, or set it too high

From the "be strong enough to stand" side comes the valid cluster: something valid is strong enough to hold up under scrutiny — a valid argument stands, a valid ticket is legally sound. invalid won't stand; validate makes it stand; validity is the quality of standing.

Add a prefix and the "being stronger" sense produces a third group:

- pre- (before, ahead) + valēre → prevail: to be stronger than the others, to come out ahead. From it, prevalent / prevailing / prevalence describe whatever is currently "winning" — the dominant, widespread thing.
- equ- (equal) + val → equivalent: of equal worth or strength.
- ambi- (both) + val → ambivalent: pulled with equal force in both directions, hence torn, of two minds.
- avail (via Old French, ad- "to" + valēre) → to be of worth to someone, to be useful; available = able to be used.

The "strength" sense also gave us courage words borrowed through French: valiant and valor — strength of heart on the battlefield. And medicine kept the "health" sense in convalesce (con- + valēscere "to grow strong") = to gradually grow strong again after illness.

Finally, one surprising member. Romans said goodbye with "Valē!" — literally the command "Be strong! / Be well!", our equivalent of "take care." That little farewell survives in valediction (vale + dicere "to say" = the saying of goodbye) and the American valedictorian, the graduate who gives the farewell speech. So the same root that prices a diamond and validates a contract also whispers the last goodbye.