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"Diente" is a form of "diente", a noun which is often translated as "tooth". "Sacar una muela" is an intransitive verb phrase which is often translated as "to take out a tooth". Learn more about the difference between "sacar una muela" and "diente" below.
sacar una muela(  
sah
-
kahr
oo
-
nah
mweh
-
lah
)An intransitive verb phrase is a phrase that combines a verb with a preposition or other particle and does not require a direct object (e.g., Everybody please stand up.).
1. (dentistry)
a. to take out a tooth 
¿Qué te pasa? ¡Qué cara de dolor tienes! - Sí, me acaban de sacar una muela.What's the matter with you? You look so much in pain! - Yes, I've just had a tooth taken out.
b. to extract a molar 
El dentista dijo que no es necesario sacar una muela.The dentist said it's not necessary to extract a molar.
c. to extract a back tooth 
Los dentistas siempre les ponen anestesia a sus pacientes cuando les sacan una muela.Dentists always anesthetize their patients when they extract a back tooth.
d. to pull a tooth 
¿Otro soldado te sacó una muela con unas tenazas? - Sí, estábamos en las trincheras. No teníamos otra cosa.Did you have a tooth pulled out by another soldier with a pair or pliers? - Yes, we were in the trenches. We didn't have anything else.
f. to pull a back tooth 
La dentista le sacó una muela a Antonio porque la tenía muy picada.Antonio had a back tooth pulled by the dentist because it was very decayed.
el diente(
dyehn
-
teh
)A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).