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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3ExpertLevel 16
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Which statement gives the deeper reason using prime exponents in perfect squares for the proof of (\sqrt{2})?

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Answer and explanation

Correct answer: In a perfect square the exponent of (2) is even

In a perfect square every prime exponent is even. In (2b^2), the exponent of (2) becoming odd explains the contradiction.

Related tags

Number-SystemsPrime-FactorizationSqrt2

Frequently asked questions

What is the correct answer to this question?

In a perfect square the exponent of (2) is even

Why is this the correct answer?

In a perfect square every prime exponent is even. In (2b^2), the exponent of (2) becoming odd explains the contradiction.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.

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10 more MCQs
  1. 1What assumption is taken first to prove the irrationality of (\sqrt{2})?
  2. 2If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  3. 3Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  4. 4From (p^2=2q^2) what conclusion is obtained about (p^2)?
  5. 5If (p^2) is even then what is the correct conclusion about (p)?
  6. 6A student sees \(\sqrt{3}\) displayed as 1.732 on a calculator and claims that \(\sqrt{3}\) is rational because the decimal ends. Which statement correctly identifies the error?
  7. 7If (p=2r) and (p^2=2q^2), which conclusion follows next?
  8. 8From (q^2=2r^2) what conclusion follows about (q)?
  9. 9What is the final contradiction in the proof that √2 is irrational?
  10. 10Which method is used in the proof of the irrationality of √2?
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