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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5MediumLevel 17

If (q^2=3k^2) is obtained in the proof of (\sqrt{3}), what is the correct conclusion for (q)?

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Answer and explanation

Correct answer: (q) is divisible by (3)

Step 1: From (q^2=3k^2), (q^2) is divisible by (3). Step 2: Since (3) is prime, (q) is also divisible by (3). Step 3: This shows a common factor in (p) and (q).

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sqrt3 proofq divisibilityclass 10

Frequently asked questions

What is the correct answer to this question?

(q) is divisible by (3)

Why is this the correct answer?

Step 1: From (q^2=3k^2), (q^2) is divisible by (3). Step 2: Since (3) is prime, (q) is also divisible by (3). Step 3: This shows a common factor in (p) and (q).

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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