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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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In the proof of (\sqrt{5}), if (\frac{p}{q}) is in lowest form, which statement is correct when (p=5k) and (q=5r) are obtained?

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Answer and explanation

Correct answer: This result is impossible because the fraction can be reduced

Step 1: (p=5k) and (q=5r) mean both have common factor (5). Step 2: Such a fraction can be reduced by (5). Step 3: Hence this is an impossible result for the lowest-form assumption.

Related tags

Sqrt5 ProofLowest Form ContradictionHard

Frequently asked questions

What is the correct answer to this question?

This result is impossible because the fraction can be reduced

Why is this the correct answer?

Step 1: (p=5k) and (q=5r) mean both have common factor (5). Step 2: Such a fraction can be reduced by (5). Step 3: Hence this is an impossible result for the lowest-form assumption.

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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