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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3MediumLevel 17
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In the proof of (\sqrt{3}), after getting (q^2=3k^2), what is the next conclusion toward final contradiction?

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Answer and explanation

Correct answer: (q) is divisible by (3)

(q^2) is divisible by (3), so (q) is also divisible by (3). This gives common factor (3) in both (p) and (q).

Related tags

Number-SystemsSqrt3Contradiction-Step

Frequently asked questions

What is the correct answer to this question?

(q) is divisible by (3)

Why is this the correct answer?

(q^2) is divisible by (3), so (q) is also divisible by (3). This gives common factor (3) in both (p) and (q).

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. 1If \(x=3-\sqrt5\), what is \(\frac1x\)?
  2. 2What assumption is taken first to prove the irrationality of (\sqrt{2})?
  3. 3If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  4. 4Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  5. 5From (p^2=2q^2) what conclusion is obtained about (p^2)?
  6. 6If (p^2) is even then what is the correct conclusion about (p)?
  7. 7A 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?
  8. 8If (p=2r) and (p^2=2q^2), which conclusion follows next?
  9. 9From (q^2=2r^2) what conclusion follows about (q)?
  10. 10What is the final contradiction in the proof that √2 is irrational?
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