Option C:
is an example of why irrational numbers are not closed under addition.
Explanation:
For a irrational number to be closed under addition, the sum of two numbers of an irrational number must also be an irrational.
Option A :
and 4 is not irrational.
From the expression, we can see that
is a rational number because it results in a rational number. That is, ![$\sqrt{4}=2$](https://tex.z-dn.net/?f=%24%5Csqrt%7B4%7D%3D2%24)
Thus, Option A is not the correct answer.
Option B :
and 1 is not irrational.
From the expression, we can see that
is a rational number.
Hence, the addition of two rational numbers results in a rational number.
Thus, Option B is not the correct answer.
Option C :
and 0 is not irrational.
From the expression, we can see that
is an irrational number because it is a non - terminating decimal number.
Hence, the addition of two irrational number is a rational number.
Therefore, the irrational numbers are not closed under addition because the addition of irrational numbers does not result in a irrational number.
Thus, Option C is the correct answer.
Option D :
and 0 is not irrational.
From the expression, we can see that 3 is a rational number.
Hence, the addition of two rational numbers results in a rational number.
Thus, Option D is not the correct answer.