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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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If (r) is prime and (r\mid x^2), what is its correct use in the proofs of (\sqrt{3}) and (\sqrt{5})?

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Answer and explanation

Correct answer: To conclude (r\mid x)

Step 1: If a prime divides a square, it also divides the original number. Step 2: In (\sqrt{3}), this rule is used for (3), and in (\sqrt{5}), for (5). Step 3: This helps get a common factor in numerator and denominator.

Related tags

Prime DivisibilityIrrationality ProofHardClass 10

Frequently asked questions

What is the correct answer to this question?

To conclude (r\mid x)

Why is this the correct answer?

Step 1: If a prime divides a square, it also divides the original number. Step 2: In (\sqrt{3}), this rule is used for (3), and in (\sqrt{5}), for (5). Step 3: This helps get a common factor in numerator and denominator.

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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