Question

In what ways is Hamlet a round character? Check all that apply. He always does the right thing, regardless of the consequences. He shows a range of emotions over the course of the play. He dies at the end of the play, as all tragic heroes do. Like a real person, he has a complicated and nuanced personality. He represents the concept of indecision.
the answer is - He shows a range of emotions over the course of the play. and 
                      - Like a real person, he has a complicated and nuanced personality.

Answer 1

He shows a range of emotions over the course of the play.
Like a real person, he has a complicated and nuanced personality. 

Hamlet's personality grows and changes over the course of the play. He allows the audience into this journey with him, and we get to see how he changes emotionally. Also, he doesn't always make the best decisions; his actions are complicated as real, round characters should be. 

Answer 2

He shows a range of emotions over the course of the play.

Hamlet experiences a wide range of emotions throughout the play, something which makes him a round character. For example, he feels pain and sadness for the death of his father. Later on in the play, he feels anger and wants to avenge for the murder of his father.  He also experiences moments of mental insanity, when his friends and family believe he is mad.

Like a real person, he has a complicated and nuanced personality.

Hamlet's personality is complicated and this contributes to the roundness of his character. Many times in the play his behaviour is unpredictable. For example, he seems that he loves his mother, but he's disappointed from her decisions and he bursts into anger against her expressed through his words to her. Hamlet is also angry with Claudius for what he has done to his father. However, Hamlet is a character which is able to show gratidute for his friends and deep love and devotion to his father. So, it resembles any other real person.