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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3ExpertLevel 65
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Why is it wrong to assume (m,n) divisible by (3) from the beginning in the proof of (\sqrt{3})?

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Answer and explanation

Correct answer: Because initially (m,n) are coprime in lowest form

Both divisible by (3) is the contradiction found at the end. Initially (\gcd(m,n)=1) is assumed.

Related tags

Number-SystemsCommon-MistakeSqrt3

Frequently asked questions

What is the correct answer to this question?

Because initially (m,n) are coprime in lowest form

Why is this the correct answer?

Both divisible by (3) is the contradiction found at the end. Initially (\gcd(m,n)=1) is assumed.

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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