Are irrational numbers closed under addition?
Understand the Problem
The question is asking whether the sum of two irrational numbers always results in an irrational number. To address this, we will consider examples where two irrational numbers are added together and analyze the results.
Answer
Irrational numbers are not closed under addition.
The final answer is that irrational numbers are not closed under addition.
Answer for screen readers
The final answer is that irrational numbers are not closed under addition.
More Information
An example that demonstrates this is the sum of √2 (an irrational number) and its negative √2, which is 0 (a rational number). This example shows that the addition of two irrational numbers can produce a rational number.
Tips
It's a common mistake to assume that since irrational numbers are complex, their arithmetic operations would also yield irrational results. Always test with specific examples.
