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

Why are (m) and (n) taken as coprime when (\sqrt{5}) is assumed rational and written as (\sqrt{5}=\frac{m}{n})?

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Answer and explanation

Correct answer: Because the fraction is taken in lowest form

Step 1: A rational number is written as a ratio of two integers. Step 2: In the proof, it is taken in lowest form, so (m) and (n) are coprime. Step 3: Later, finding a common factor gives the contradiction.

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sqrt5 proofcoprimerational formclass 10

Frequently asked questions

What is the correct answer to this question?

Because the fraction is taken in lowest form

Why is this the correct answer?

Step 1: A rational number is written as a ratio of two integers. Step 2: In the proof, it is taken in lowest form, so (m) and (n) are coprime. Step 3: Later, finding a common factor gives the 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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