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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3ExpertLevel 65
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If (p) is not divisible by (3) in the proof of (\sqrt{3}), what contradiction follows from (p^2=3q^2)?

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Answer and explanation

Correct answer: (p^2) should not be divisible by (3), but the equation shows it is divisible

If (p) has no factor (3), then (p^2) also has no factor (3). But the equation shows (p^2) divisible by (3).

Related tags

Number-SystemsDivisibility-Sqrt3Expert

Frequently asked questions

What is the correct answer to this question?

(p^2) should not be divisible by (3), but the equation shows it is divisible

Why is this the correct answer?

If (p) has no factor (3), then (p^2) also has no factor (3). But the equation shows (p^2) divisible by (3).

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. 1If \(x=3-\sqrt5\), what is \(\frac1x\)?
  2. 2What assumption is taken first to prove the irrationality of (\sqrt{2})?
  3. 3If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  4. 4Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  5. 5From (p^2=2q^2) what conclusion is obtained about (p^2)?
  6. 6If (p^2) is even then what is the correct conclusion about (p)?
  7. 7A 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?
  8. 8If (p=2r) and (p^2=2q^2), which conclusion follows next?
  9. 9From (q^2=2r^2) what conclusion follows about (q)?
  10. 10What is the final contradiction in the proof that √2 is irrational?
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