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1 answer:
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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.