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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5ExpertLevel 17
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What is the best exam tip related to the irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?

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Answer and explanation

Correct answer: Write lowest rational form, squaring, prime divisibility, and coprime contradiction in order

Step 1: First write (\frac{p}{q}) in lowest form. Step 2: Then square and use the related prime factor to show divisibility of both numerator and denominator. Step 3: Finally state the contradiction with coprimality clearly.

Related tags

Real-NumbersIrrationalityExam-TipProof-Writing

Frequently asked questions

What is the correct answer to this question?

Write lowest rational form, squaring, prime divisibility, and coprime contradiction in order

Why is this the correct answer?

Step 1: First write (\frac{p}{q}) in lowest form. Step 2: Then square and use the related prime factor to show divisibility of both numerator and denominator. Step 3: Finally state the contradiction with coprimality clearly.

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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