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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3MediumLevel 17
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What is the correct combined conclusion of the proofs of both (\sqrt{2}) and (\sqrt{3})?

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Answer and explanation

Correct answer: Assuming either rational gives contradiction, so both are irrational

In both proofs, the rational assumption clashes with the coprime condition. Therefore both (\sqrt{2}) and (\sqrt{3}) are irrational.

Related tags

Number-SystemsIrrationality-ProofCombined-Conclusion

Frequently asked questions

What is the correct answer to this question?

Assuming either rational gives contradiction, so both are irrational

Why is this the correct answer?

In both proofs, the rational assumption clashes with the coprime condition. Therefore both (\sqrt{2}) and (\sqrt{3}) are irrational.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.

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10 more MCQs
  1. 1What assumption is taken first to prove the irrationality of (\sqrt{2})?
  2. 2If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  3. 3Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  4. 4From (p^2=2q^2) what conclusion is obtained about (p^2)?
  5. 5If (p^2) is even then what is the correct conclusion about (p)?
  6. 6A student sees \(\sqrt{3}\) displayed as 1.732 on a calculator and claims that \(\sqrt{3}\) is rational because the decimal ends. Which statement correctly identifies the error?
  7. 7If (p=2r) and (p^2=2q^2), which conclusion follows next?
  8. 8From (q^2=2r^2) what conclusion follows about (q)?
  9. 9What is the final contradiction in the proof that √2 is irrational?
  10. 10Which method is used in the proof of the irrationality of √2?
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