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Subjects
Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 16
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In the proof of (\sqrt{5}), (p) is proved divisible by (5) from (p^2=5q^2). What does this depend on?

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Answer and explanation

Correct answer: On (5) being prime

Step 1: From (p^2=5q^2), (p^2) is divisible by (5). Step 2: If a square is divisible by a prime, the original number is also divisible by that prime. Step 3: So (5) being prime is the main basis here.

Related tags

Sqrt5 ProofPrime BasisHardClass 10

Frequently asked questions

What is the correct answer to this question?

On (5) being prime

Why is this the correct answer?

Step 1: From (p^2=5q^2), (p^2) is divisible by (5). Step 2: If a square is divisible by a prime, the original number is also divisible by that prime. Step 3: So (5) being prime is the main basis here.

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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