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

Which option is the correct short reason for the irrationality of (\sqrt{3})?

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Answer and explanation

Correct answer: Assuming rational makes both numerator and denominator divisible by (3)

Step 1: Assuming (\sqrt{3}=\frac{a}{b}) and squaring gives (a^2=3b^2). Step 2: This makes both (a) and (b) divisible by (3). Step 3: This is impossible in a lowest-form fraction.

Tags

sqrt3 explanationirrationalityclass 10

Frequently asked questions

What is the correct answer to this question?

Assuming rational makes both numerator and denominator divisible by (3)

Why is this the correct answer?

Step 1: Assuming (\sqrt{3}=\frac{a}{b}) and squaring gives (a^2=3b^2). Step 2: This makes both (a) and (b) divisible by (3). Step 3: This is impossible in a lowest-form fraction.

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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