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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 17
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While writing the final line in all three proofs, which sentence is the safest?

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Answer and explanation

Correct answer: This contradicts our rational assumption, hence the given number is irrational

Step 1: All three proofs start with a rational assumption. Step 2: At the end, a contradiction is obtained from the coprime condition. Step 3: Therefore the final line should clearly state contradiction and irrationality.

Related tags

Final ConclusionExam WritingHardClass 10

Frequently asked questions

What is the correct answer to this question?

This contradicts our rational assumption, hence the given number is irrational

Why is this the correct answer?

Step 1: All three proofs start with a rational assumption. Step 2: At the end, a contradiction is obtained from the coprime condition. Step 3: Therefore the final line should clearly state contradiction and irrationality.

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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