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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5ExpertLevel 17
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Which option states the correct final contradiction in the proof for (\sqrt{3})?

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Answer and explanation

Correct answer: (a) and (b) were coprime, but both turned out divisible by (3)

Step 1: Coprime means there is no common factor except (1). Step 2: Both being divisible by (3) gives a common factor. Step 3: This contradiction proves (\sqrt{3}) irrational.

Related tags

Real-NumbersRoot3Final-ContradictionCoprime

Frequently asked questions

What is the correct answer to this question?

(a) and (b) were coprime, but both turned out divisible by (3)

Why is this the correct answer?

Step 1: Coprime means there is no common factor except (1). Step 2: Both being divisible by (3) gives a common factor. Step 3: This contradiction proves (\sqrt{3}) irrational.

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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