Quick answer
"Figure out" is a transitive verb phrase which is often translated as "resolver", and "ascertain" is a transitive verb which is often translated as "establecer". Learn more about the difference between "figure out" and "ascertain" below.
figure out(
A transitive verb phrase is a phrase that combines a verb with a preposition or other particle and requires a direct object (e.g. Take out the trash.).
transitive verb phrase
1. (to solve)
a. resolver
The first one to figure out the problem gets a prize.El primero que resuelva el problema, se gana un premio.
b. descifrar
Sherlock Holmes figured out the mystery of the stolen jewelry.Sherlock Holmes descifró el misterio de las joyas robadas.
c. calcular (in mathematics)
Figure out the sum of the inner angles of the polygon.Calcula la suma de los ángulos interiores del polígono.
2. (to understand)
a. entender
Today she didn't say hi to me. I can't figure her out.Hoy no me saludó. Me cuesta entenderla.
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A transitive verb is a verb that requires a direct object (e.g. I bought a book.).
1. (general)
a. establecer
The judge ordered an inquiry into the accident in an attempt to ascertain the circumstances surrounding it.El juez pidió que se abriera una investigación sobre el accidente, en un intento por establecer las circunstancias que lo rodearon.
b. determinar
It had proved impossible to ascertain the cause of death.Había resultado imposible determinar la causa de la muerte.
c. averiguar
I think we need to ascertain what's really going on before making a judgment.Yo creo que tenemos que averiguar qué está pasando de verdad antes de formarnos un juicio.
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