Question

Can you check my answer?

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

I was thinking:
–3 + 3 = 0, and 0 is not irrational
because it came up with a different number besides 3.,

Answer 1

-3+3 = 0 is an example of adding two rational numbers to get another rational number.

-3 = -3/1
3 = 3/1
0 = 0/1
each can be written as a fraction of whole numbers, so that's why they are rational

The actual answer is choice C

We are adding the square root of 10, written sqrt(10) in shorthand, to the negative version of the same number. Doing so leads to 0. This is using the property x + (-x) = 0. The left hand side of choice C has two irrational numbers. They add to 0 on the right hand side which is rational. The fact that we added two irrational numbers to get an rational result indicates that irrational numbers are not closed under addition.