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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5MediumLevel 18
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Which statement correctly completes the proof of (\sqrt{2}), (\sqrt{3}), or (\sqrt{5}) in the final line?

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Answer and explanation

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

Step 1: In the proof, the rational assumption leads to an impossible common factor. Step 2: This contradicts the assumption. Step 3: So the final line should clearly state contradiction and irrationality.

Related tags

Final StatementExam ProofClass 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: In the proof, the rational assumption leads to an impossible common factor. Step 2: This contradicts the assumption. Step 3: So 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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