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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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In the proof of (\sqrt{2}), after getting (p^2=2q^2), which statement is correct but does not yet complete the proof?

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Answer and explanation

Correct answer: (p) is even

Step 1: From (p^2=2q^2), (p^2) and then (p) are proved even. Step 2: But to complete the proof, (q) must also be shown even. Step 3: Only then a contradiction arises through common factor (2).

Related tags

Sqrt2 ProofIncomplete StepHardClass 10

Frequently asked questions

What is the correct answer to this question?

(p) is even

Why is this the correct answer?

Step 1: From (p^2=2q^2), (p^2) and then (p) are proved even. Step 2: But to complete the proof, (q) must also be shown even. Step 3: Only then a contradiction arises through common factor (2).

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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