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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 16
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Which contradiction appears in the proof of (\sqrt{5})?

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Answer and explanation

Correct answer: Both (p) and (q) are found divisible by (5)

Step 1: We started by taking (p) and (q) as coprime. Step 2: The proof shows both are divisible by (5). Step 3: Two coprime numbers cannot have (5) as a common factor, so this is a contradiction.

Related tags

ContradictionSqrt5 ProofClass 10

Frequently asked questions

What is the correct answer to this question?

Both (p) and (q) are found divisible by (5)

Why is this the correct answer?

Step 1: We started by taking (p) and (q) as coprime. Step 2: The proof shows both are divisible by (5). Step 3: Two coprime numbers cannot have (5) as a common factor, so this is a contradiction.

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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