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

While proving the irrationality of (\sqrt{3}), (p^2=3q^2) is obtained. Which conclusion about (p) with reason is correct?

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Answer and explanation

Correct answer: (p) is divisible by (3) because (p^2) is divisible by (3) and (3) is prime

Step 1: From (p^2=3q^2), (p^2) is divisible by (3). Step 2: Since (3) is prime, (p) is also divisible by (3). Step 3: Apply the prime factor rule to the correct number.

Tags

sqrt3 proofprime divisibilityreal numbersclass 10

Frequently asked questions

What is the correct answer to this question?

(p) is divisible by (3) because (p^2) is divisible by (3) and (3) is prime

Why is this the correct answer?

Step 1: From (p^2=3q^2), (p^2) is divisible by (3). Step 2: Since (3) is prime, (p) is also divisible by (3). Step 3: Apply the prime factor rule to the correct number.

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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