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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 17
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In the proof of (\sqrt{3}), if both (a) and (b) are found divisible by (3), which condition is broken?

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Answer and explanation

Correct answer: The condition of being coprime

Step 1: Coprime numbers have no common factor except (1). Step 2: If both (a) and (b) are divisible by (3), they have common factor (3). Step 3: This is the contradiction in the proof.

Related tags

Sqrt3 ProofCoprimeContradictionClass 10

Frequently asked questions

What is the correct answer to this question?

The condition of being coprime

Why is this the correct answer?

Step 1: Coprime numbers have no common factor except (1). Step 2: If both (a) and (b) are divisible by (3), they have common factor (3). Step 3: This is the contradiction in the proof.

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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