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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3EasyLevel 20
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Which statement is correct in proving irrationality of (\sqrt{3})?

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Answer and explanation

Correct answer: If (p^2) is divisible by (3) then (p) is divisible by (3)

If prime (3) divides the square, it divides the number too. This is the main step in the proof.

Related tags

Number-SystemsSqrt3Key-Fact

Frequently asked questions

What is the correct answer to this question?

If (p^2) is divisible by (3) then (p) is divisible by (3)

Why is this the correct answer?

If prime (3) divides the square, it divides the number too. This is the main step in the proof.

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 is the simplified form of √242 − √128?
  2. 2If \(x=3-\sqrt5\), what is \(\frac1x\)?
  3. 3What assumption is taken first to prove the irrationality of (\sqrt{2})?
  4. 4If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  5. 5Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  6. 6From (p^2=2q^2) what conclusion is obtained about (p^2)?
  7. 7If (p^2) is even then what is the correct conclusion about (p)?
  8. 8A 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?
  9. 9If (p=2r) and (p^2=2q^2), which conclusion follows next?
  10. 10From (q^2=2r^2) what conclusion follows about (q)?
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