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A student claims that the sum of two irrational numbers is always irrational. Which example proves the claim wrong?
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Answer and explanation
Correct answer: \(\sqrt{2}+(-\sqrt{2})=0\)
Both \(\sqrt{2}\) and \(-\sqrt{2}\) are irrational, but their sum is \(0\), which is rational. Hence the claim is not always true. Exam tip: test an “always” statement by finding one counterexample.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{2}+(-\sqrt{2})=0\)
Why is this the correct answer?
Both \(\sqrt{2}\) and \(-\sqrt{2}\) are irrational, but their sum is \(0\), which is rational. Hence the claim is not always true. Exam tip: test an “always” statement by finding one counterexample.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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