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

If (\sqrt{5}=\frac{m}{n}) and (m^2=5n^2), what is the first correct conclusion about (m^2)?

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Answer and explanation

Correct answer: (m^2) is divisible by (5)

Step 1: In (m^2=5n^2), the right side has factor (5). Step 2: Therefore (m^2) is divisible by (5). Step 3: First write divisibility of the square, then conclude divisibility of (m).

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sqrt5 proofdivisibilityclass 10

Frequently asked questions

What is the correct answer to this question?

(m^2) is divisible by (5)

Why is this the correct answer?

Step 1: In (m^2=5n^2), the right side has factor (5). Step 2: Therefore (m^2) is divisible by (5). Step 3: First write divisibility of the square, then conclude divisibility of (m).

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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