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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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Which option tells the role of assuming (\frac{p}{q}) in lowest form in the proof of (\sqrt{2})?

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Answer and explanation

Correct answer: To show contradiction when both (p) and (q) are later found even

Step 1: In lowest form, (p) and (q) are coprime. Step 2: The proof shows both (p) and (q) are even. Step 3: Both being even breaks the lowest-form condition.

Related tags

Sqrt2 ProofLowest Form RoleHardClass 10

Frequently asked questions

What is the correct answer to this question?

To show contradiction when both (p) and (q) are later found even

Why is this the correct answer?

Step 1: In lowest form, (p) and (q) are coprime. Step 2: The proof shows both (p) and (q) are even. Step 3: Both being even breaks the lowest-form condition.

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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