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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3ExpertLevel 16
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In the proof of (\sqrt{2}), if (a,b) are assumed coprime and later (a=2r) and (b=2s) are obtained, which conclusion is most precise?

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Answer and explanation

Correct answer: (\frac{a}{b}) can be reduced to (\frac{r}{s}), so the initial lowest form was impossible

Since both have common factor (2), the fraction can be reduced. This contradicts the coprime lowest form.

Related tags

Number-SystemsExpert-ProofSqrt2Reduction

Frequently asked questions

What is the correct answer to this question?

(\frac{a}{b}) can be reduced to (\frac{r}{s}), so the initial lowest form was impossible

Why is this the correct answer?

Since both have common factor (2), the fraction can be reduced. This contradicts the coprime lowest form.

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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