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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 18
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Which option gives the correct order of the proof of (\sqrt{2})?

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Answer and explanation

Correct answer: Assume rational, square, find both even, contradiction

Step 1: First assume (\sqrt{2}) is rational. Step 2: After squaring, both (p) and (q) are found even. Step 3: Both being even contradicts the coprime condition.

Related tags

Proof OrderSqrt2Class 10

Frequently asked questions

What is the correct answer to this question?

Assume rational, square, find both even, contradiction

Why is this the correct answer?

Step 1: First assume (\sqrt{2}) is rational. Step 2: After squaring, both (p) and (q) are found even. Step 3: Both being even contradicts the coprime condition.

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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