Etymology
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Valerie 
fem. proper name, French, from Latin Valeria, fem. of Valerius, name of a Roman gens, from valere "to be strong" (from PIE root *wal- "to be strong").
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valerian (n.)
plant of Eurasia, cultivated for its medicinal root, late 14c., from Old French valeriane "wild valerian" (13c.), apparently from feminine singular of Latin adjective Valerianus, from the personal name Valerius (see Valerie); but Weekley writes, "some of the German and Scand. forms of the name point rather to connection with the saga-hero Wieland."
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*wal- 

Proto-Indo-European root meaning "to be strong."

It forms all or part of: ambivalence; Arnold; avail; bivalent; convalesce; countervail; Donald; equivalent; evaluation; Gerald; Harold; invalid (adj.1) "not strong, infirm;" invalid (adj.2) "of no legal force;" Isold; multivalent; polyvalent; prevalent; prevail; Reynold; Ronald; valediction; valence; Valerie; valetudinarian; valiance; valiant; valid; valor; value; Vladimir; Walter; wield.

It is the hypothetical source of/evidence for its existence is provided by: Latin valere "be strong, be well, be worth;" Old Church Slavonic vlasti "to rule over;" Lithuanian valdyti "to have power;" Celtic *walos- "ruler," Old Irish flaith "dominion," Welsh gallu "to be able;" Old English wealdan "to rule," Old High German -walt, -wald "power" (in personal names), Old Norse valdr "ruler."

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