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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5ExpertLevel 18

In the proof for (\sqrt{5}), both (a) and (b) are found divisible by (5). What type of result is this?

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Answer and explanation

Correct answer: Contradictory result

Step 1: At the beginning, (a) and (b) were assumed coprime. Step 2: Both being divisible by (5) gives a common factor. Step 3: Therefore this is a contradictory result, and the rational assumption is false.

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real-numbersroot5contradictionresult-type

Frequently asked questions

What is the correct answer to this question?

Contradictory result

Why is this the correct answer?

Step 1: At the beginning, (a) and (b) were assumed coprime. Step 2: Both being divisible by (5) gives a common factor. Step 3: Therefore this is a contradictory result, and the rational assumption is false.

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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