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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 17
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Which statement tells the real role of squaring in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?

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Answer and explanation

Correct answer: To remove the square root and create a divisibility equation

Step 1: Squaring (\sqrt{n}=\frac{p}{q}) removes (\sqrt{n}). Step 2: This creates an equation like (p^2=nq^2). Step 3: Divisibility and contradiction start from this equation.

Related tags

Squaring RoleProof StructureHardClass 10

Frequently asked questions

What is the correct answer to this question?

To remove the square root and create a divisibility equation

Why is this the correct answer?

Step 1: Squaring (\sqrt{n}=\frac{p}{q}) removes (\sqrt{n}). Step 2: This creates an equation like (p^2=nq^2). Step 3: Divisibility and contradiction start from this equation.

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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