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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 18
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Which option correctly explains proof by contradiction in irrationality proofs?

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Answer and explanation

Correct answer: Assume the opposite of what is to be proved and show an impossible result

Step 1: In proof by contradiction, we begin with the opposite assumption. Step 2: Then we reach a result that conflicts with the given condition. Step 3: The proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}) follow this structure.

Related tags

Real-NumbersContradiction-MethodIrrationalityProofHard

Frequently asked questions

What is the correct answer to this question?

Assume the opposite of what is to be proved and show an impossible result

Why is this the correct answer?

Step 1: In proof by contradiction, we begin with the opposite assumption. Step 2: Then we reach a result that conflicts with the given condition. Step 3: The proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}) follow this structure.

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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