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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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Which option states the final contradiction in the proof of (\sqrt{2}) in correct language?

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Answer and explanation

Correct answer: (p) and (q) were assumed coprime, but both turned out divisible by (2)

Step 1: At the start, (\frac{p}{q}) is taken in lowest form, so (p) and (q) are assumed coprime. Step 2: The proof shows both are divisible by (2). Step 3: This is the clear and correct contradiction.

Related tags

Sqrt2 ProofFinal ContradictionHardClass 10

Frequently asked questions

What is the correct answer to this question?

(p) and (q) were assumed coprime, but both turned out divisible by (2)

Why is this the correct answer?

Step 1: At the start, (\frac{p}{q}) is taken in lowest form, so (p) and (q) are assumed coprime. Step 2: The proof shows both are divisible by (2). Step 3: This is the clear and correct 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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