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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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Which statement shows a logical weakness in the proof of (\sqrt{2})?

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Answer and explanation

Correct answer: (p) is even, so (q) is also even without any substitution

Step 1: (p) being even does not automatically make (q) even. Step 2: To prove (q) even, (p=2k) must be substituted in the original equation. Step 3: Writing conclusions without support weakens the proof.

Related tags

Sqrt2 ProofLogical WeaknessHardClass 10

Frequently asked questions

What is the correct answer to this question?

(p) is even, so (q) is also even without any substitution

Why is this the correct answer?

Step 1: (p) being even does not automatically make (q) even. Step 2: To prove (q) even, (p=2k) must be substituted in the original equation. Step 3: Writing conclusions without support weakens the proof.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.

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10 more MCQs
  1. 1Which assumption is taken first to prove that (\sqrt{2}) is irrational?
  2. 2If (\sqrt{2}=\frac{p}{q}), what is obtained after squaring both sides?
  3. 3From the equation (p^2=2q^2), what do we learn about (p^2)?
  4. 4If (p^2) is even, which conclusion about (p) is correct?
  5. 5If (p) is even, in which form can (p) be written?
  6. 6What conclusion is obtained by putting (p=2k) in (p^2=2q^2)?
  7. 7What is the final contradiction in the proof of (\sqrt{2})?
  8. 8What is the correct final conclusion of the proof of (\sqrt{2})?
  9. 9If (\sqrt{3}) is assumed rational, in which form is it written?
  10. 10If (\sqrt{3}=\frac{p}{q}), which equation is obtained after squaring?
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