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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5MediumLevel 18
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Which option gives the correct final reason in the proof of (\sqrt{2})?

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Answer and explanation

Correct answer: Both (p) and (q) are even, so they cannot be coprime

Step 1: If both are even, both have common factor (2). Step 2: This cannot happen for coprime numbers. Step 3: This final reason proves (\sqrt{2}) irrational.

Related tags

Sqrt2 ProofFinal ReasonClass 10

Frequently asked questions

What is the correct answer to this question?

Both (p) and (q) are even, so they cannot be coprime

Why is this the correct answer?

Step 1: If both are even, both have common factor (2). Step 2: This cannot happen for coprime numbers. Step 3: This final reason proves (\sqrt{2}) irrational.

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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