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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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If in the proof of (\sqrt{3}), both (p) and (q) are found divisible by (3), which statement about (\frac{p}{q}) is correct?

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Answer and explanation

Correct answer: It cannot be in lowest form

Step 1: If both are divisible by (3), numerator and denominator have common factor (3). Step 2: Such a fraction can be reduced further by (3). Step 3: Hence it cannot be in lowest form.

Related tags

Sqrt3 ProofFraction FormHardClass 10

Frequently asked questions

What is the correct answer to this question?

It cannot be in lowest form

Why is this the correct answer?

Step 1: If both are divisible by (3), numerator and denominator have common factor (3). Step 2: Such a fraction can be reduced further by (3). Step 3: Hence it cannot be in 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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