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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 18
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Which statement is most essential in proving the irrationality of (\sqrt{3})?

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Answer and explanation

Correct answer: If (3) divides (p^2), then (3) divides (p)

Step 1: Assuming (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2). Step 2: The key step is using (3\mid p^2\Rightarrow 3\mid p). Step 3: Writing this prime-number property clearly helps in scoring well.

Related tags

Real-NumbersIrrationalityRoot3Prime-DivisibilityHard

Frequently asked questions

What is the correct answer to this question?

If (3) divides (p^2), then (3) divides (p)

Why is this the correct answer?

Step 1: Assuming (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2). Step 2: The key step is using (3\mid p^2\Rightarrow 3\mid p). Step 3: Writing this prime-number property clearly helps in scoring well.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.

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10 more MCQs
  1. 1Which assumption is taken first to prove that (\sqrt{2}) is irrational?
  2. 2If (\sqrt{2}=\frac{p}{q}), what is obtained after squaring both sides?
  3. 3From the equation (p^2=2q^2), what do we learn about (p^2)?
  4. 4If (p^2) is even, which conclusion about (p) is correct?
  5. 5If (p) is even, in which form can (p) be written?
  6. 6What conclusion is obtained by putting (p=2k) in (p^2=2q^2)?
  7. 7What is the final contradiction in the proof of (\sqrt{2})?
  8. 8What is the correct final conclusion of the proof of (\sqrt{2})?
  9. 9If (\sqrt{3}) is assumed rational, in which form is it written?
  10. 10If (\sqrt{3}=\frac{p}{q}), which equation is obtained after squaring?
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