Acuity

acuity is made up of acu- meaning "sharp" and the Latin suffix -ity which means "the state, condition, or quality of being". Thus, acuity means "the state or condition of being sharp", but it is applied to sharpness or acuteness of the mind or senses.
The professor has great mental acuity.

Root: Acu-, Acr-

The Latin root acu- or acr- means "sharp". You should sharpen your vocabulary with the five core words in which the root acu- or acr- appear: acrid, acrimony, acuity, acumen, acute.