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

If (a^2=3b^2), what conclusion about (a) is taken in the proof of (\sqrt{3})?

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Answer and explanation

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

Step 1: From (a^2=3b^2), (a^2) is divisible by (3). Step 2: Since (3) is prime, (a) is also divisible by (3). Step 3: Remember this rule from square to original number.

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sqrt3 proofprime divisibilityclass 10

Frequently asked questions

What is the correct answer to this question?

(a) is divisible by (3)

Why is this the correct answer?

Step 1: From (a^2=3b^2), (a^2) is divisible by (3). Step 2: Since (3) is prime, (a) is also divisible by (3). Step 3: Remember this rule from square to original 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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