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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5MediumLevel 17
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Which option gives the correct final reason in the proof of (\sqrt{5})?

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Answer and explanation

Correct answer: Both (p) and (q) are divisible by (5), so they cannot be coprime

Step 1: In the proof, both (p) and (q) are found divisible by (5). Step 2: This means their common factor is (5). Step 3: This breaks the condition of being coprime.

Related tags

Sqrt5 ProofFinal ReasonClass 10

Frequently asked questions

What is the correct answer to this question?

Both (p) and (q) are divisible by (5), so they cannot be coprime

Why is this the correct answer?

Step 1: In the proof, both (p) and (q) are found divisible by (5). Step 2: This means their common factor is (5). Step 3: This breaks the condition of being coprime.

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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