*u̯al-

The core idea of this root was:

being strong, powerful

This idea went straight into the Latin verb valere, and it broadened toward the idea of being legit and having value.
This verb is the origin of a whole range of words like valor, valid, value, equivalent and prevail.
Besides this branch, the root is also the origin of to wield and of a bunch of well known names like Arnold, Donald, Ronald, Walter, Volodymyr and Valerie.

Here’s an (incomplete) overview of the English relatives:

• wield (“rule, having power over”)
• valor (“power”)
• valid, validate,… (“having power”)
• value, evaluate, DFV… (a form of power basically)
• ambivalent (“multiple values”)
• equivalent (“equal value”)
• prevalent (“power in front, dominating”)
• prevail (“power through”)
• Donald (“deep value”… I know someone who would get an orgasm over this)
• Ronald (“ruling power”)
• Arnold (“eagle power”)
• Volodymyr, Vladimir (“strong peace”… irony is strong)
• Gerald (“spear wielder”)
• Harold (“army power”)
• Walter (“ruler or army”)
• Valerie (“the powerful, the worthy”)