Which of the following is an example of why irrational numbers are not closed under addition?
StartRoot 4 EndRoot + StartRoot 4 EndRoot = 2 + 2 = 4, and 4 is not irrational
One-half + one-half = 1, and 1 is not irrational
StartRoot 10 EndRoot + (negative StartRoot 10 EndRoot) = 0, and 0 is not irrational
–3 + 3 = 0, and 0 is not irrational

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,

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.

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step-by-step explanation: