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

Which option explains why (\sqrt{2}) cannot be rational?

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Answer and explanation

Correct answer: Assuming rational makes numerator and denominator of a lowest-form fraction both even

Step 1: Assuming rational, we write (\sqrt{2}=\frac{a}{b}) in lowest form. Step 2: The proof shows both (a) and (b) are even. Step 3: This contradicts lowest form, so (\sqrt{2}) cannot be rational.

Tags

sqrt2 explanationirrationalityclass 10

Frequently asked questions

What is the correct answer to this question?

Assuming rational makes numerator and denominator of a lowest-form fraction both even

Why is this the correct answer?

Step 1: Assuming rational, we write (\sqrt{2}=\frac{a}{b}) in lowest form. Step 2: The proof shows both (a) and (b) are even. Step 3: This contradicts lowest form, so (\sqrt{2}) cannot be rational.

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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