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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 18
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If the rational assumption leads to a contradiction, what is the conclusion about the original statement?

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Answer and explanation

Correct answer: The original statement is true

Step 1: In contradiction, we work with the opposite assumption. Step 2: If that assumption becomes impossible, the original statement is true. Step 3: So when rationality fails, irrationality is proved.

Related tags

Contradiction LogicProofClass 10

Frequently asked questions

What is the correct answer to this question?

The original statement is true

Why is this the correct answer?

Step 1: In contradiction, we work with the opposite assumption. Step 2: If that assumption becomes impossible, the original statement is true. Step 3: So when rationality fails, irrationality is proved.

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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