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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 18
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If both (p) and (q) are divisible by (5), what happens to their being coprime?

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Answer and explanation

Correct answer: They will not remain coprime

Step 1: If both are divisible by (5), then (5) is a common factor. Step 2: Coprime numbers should not have a common factor other than (1). Step 3: So this situation goes against being coprime.

Related tags

CoprimeDivisible By 5Sqrt5Class 10

Frequently asked questions

What is the correct answer to this question?

They will not remain coprime

Why is this the correct answer?

Step 1: If both are divisible by (5), then (5) is a common factor. Step 2: Coprime numbers should not have a common factor other than (1). Step 3: So this situation goes against being coprime.

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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