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Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3MediumLevel 17
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In the proof of (\sqrt{3}), why can we write (p=3k) from (p^2=3q^2)?

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Answer and explanation

Correct answer: Because (p^2) is divisible by (3), so (p) is divisible by (3)

If prime (3) divides the square, it also divides the number. Therefore (p) is written as (3k).

Related tags

Number-SystemsSqrt3Divisibility

Frequently asked questions

What is the correct answer to this question?

Because (p^2) is divisible by (3), so (p) is divisible by (3)

Why is this the correct answer?

If prime (3) divides the square, it also divides the number. Therefore (p) is written as (3k).

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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