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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 17
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Which statement leaves the proof of (\sqrt{5}) incomplete?

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Answer and explanation

Correct answer: Stopping after only writing (p^2=5q^2)

Step 1: (p^2=5q^2) is only a middle step. Step 2: After this, both (p) and (q) must be shown divisible by (5). Step 3: Without contradiction and final conclusion, the proof is incomplete.

Related tags

Sqrt5 ProofIncomplete ProofHardClass 10

Frequently asked questions

What is the correct answer to this question?

Stopping after only writing (p^2=5q^2)

Why is this the correct answer?

Step 1: (p^2=5q^2) is only a middle step. Step 2: After this, both (p) and (q) must be shown divisible by (5). Step 3: Without contradiction and final conclusion, the proof is incomplete.

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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