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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 18
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Which method is common in proving the irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?

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Answer and explanation

Correct answer: Method of contradiction

Step 1: In all three proofs, the number is first assumed rational. Step 2: Then a contradiction is shown using the coprime condition. Step 3: Therefore it is called the method of contradiction.

Related tags

Method Of ContradictionIrrationalityClass 10

Frequently asked questions

What is the correct answer to this question?

Method of contradiction

Why is this the correct answer?

Step 1: In all three proofs, the number is first assumed rational. Step 2: Then a contradiction is shown using the coprime condition. Step 3: Therefore it is called the method of 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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