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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 18
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Which option best describes the common idea in the proofs of (\sqrt{3}) and (\sqrt{5})?

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Answer and explanation

Correct answer: Assume rational and show the same prime factor in both numerator and denominator

Step 1: Factor (3) works in (\sqrt{3}) and factor (5) works in (\sqrt{5}). Step 2: The rational assumption makes that same factor appear in both numerator and denominator. Step 3: This common factor contradicts lowest form.

Related tags

Sqrt3 Sqrt5Common IdeaIrrationality ProofClass 10

Frequently asked questions

What is the correct answer to this question?

Assume rational and show the same prime factor in both numerator and denominator

Why is this the correct answer?

Step 1: Factor (3) works in (\sqrt{3}) and factor (5) works in (\sqrt{5}). Step 2: The rational assumption makes that same factor appear in both numerator and denominator. Step 3: This common factor contradicts lowest form.

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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