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

Why are results like (a=5k) and (b=5l) a contradiction in the proof of (\sqrt{5})?

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Answer and explanation

Correct answer: Because (a) and (b) were assumed coprime in lowest form

Step 1: (a=5k) and (b=5l) mean both are divisible by (5). Step 2: But (a) and (b) were assumed coprime at the beginning. Step 3: Hence this result gives a contradiction.

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sqrt5 proofcontradictionclass 10

Frequently asked questions

What is the correct answer to this question?

Because (a) and (b) were assumed coprime in lowest form

Why is this the correct answer?

Step 1: (a=5k) and (b=5l) mean both are divisible by (5). Step 2: But (a) and (b) were assumed coprime at the beginning. Step 3: Hence this result gives a contradiction.

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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