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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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Why is it necessary to assume (p) and (q) coprime while proving (\sqrt{5}) irrational?

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Answer and explanation

Correct answer: So that finding common factor (5) in both gives a clear contradiction

Step 1: A rational number is written as a lowest-form fraction, so (p) and (q) are coprime. Step 2: The proof shows both divisible by (5). Step 3: This gives a clear contradiction to the coprime condition.

Related tags

Sqrt5 ProofCoprime NecessityHardClass 10

Frequently asked questions

What is the correct answer to this question?

So that finding common factor (5) in both gives a clear contradiction

Why is this the correct answer?

Step 1: A rational number is written as a lowest-form fraction, so (p) and (q) are coprime. Step 2: The proof shows both divisible by (5). Step 3: This gives a clear contradiction to the coprime condition.

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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