Which of the following is an example of why irrational numbers are 'not' closed under addition?

√4 + √4 = 2 + 2 = 4, and 4 is not irrantonal
1/2 + 1/2 = 1, and 1 is not irrational
√10 + (-√10) = 0, and 0 is not irrational
-3 + 3 = 0, and 0 is not irrational

To show that irrational numbers are not closed under addition we need to find 2 irrational numbers which sum gives us NON irrational number (rational number)

First option isn't true because we have to start with irrational numbers and √4 = 2 is rational number.

second option also isnt true because again we have to start with irrational numbers and we are starting with 1/2 which is rational.

Third one is true

√10 and -√10 are 2 irrational numbers which some is 0 which is rational.

last one isn't true because of same reason as 1 and 2 options.

Answer is third option.