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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3ExpertLevel 16
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Why is it necessary to prove (q) divisible by (3) after taking (p=3r) in the proof of (\sqrt{3})?

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Answer and explanation

Correct answer: Because only then common factor (3) will appear in (p) and (q)

Only (p) being divisible by (3) is not a contradiction. If (q) is also divisible by (3), the coprime condition breaks.

Related tags

Number-SystemsProof-CompletenessSqrt3

Frequently asked questions

What is the correct answer to this question?

Because only then common factor (3) will appear in (p) and (q)

Why is this the correct answer?

Only (p) being divisible by (3) is not a contradiction. If (q) is also divisible by (3), the coprime condition breaks.

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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