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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 18
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If a fraction is in lowest form, what is true about its numerator and denominator?

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Answer and explanation

Correct answer: They are coprime

Step 1: Lowest form means the fraction cannot be reduced further. Step 2: So the numerator and denominator have only (1) as a common factor. Step 3: This fact is important in irrationality proofs.

Related tags

Lowest FormCoprimeFractionClass 10

Frequently asked questions

What is the correct answer to this question?

They are coprime

Why is this the correct answer?

Step 1: Lowest form means the fraction cannot be reduced further. Step 2: So the numerator and denominator have only (1) as a common factor. Step 3: This fact is important in irrationality proofs.

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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