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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}), if a student directly writes from (p^2=3q^2) that (q) is divisible by (3), what is the correct comment?

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Answer and explanation

Correct answer: It is incomplete because (p) must be proved divisible by (3) first

First (p) is proved divisible by (3) from (p^2). Then after putting (p=3k), the conclusion for (q) follows.

Related tags

Number-SystemsSqrt3Error-Analysis

Frequently asked questions

What is the correct answer to this question?

It is incomplete because (p) must be proved divisible by (3) first

Why is this the correct answer?

First (p) is proved divisible by (3) from (p^2). Then after putting (p=3k), the conclusion for (q) follows.

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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