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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5MediumLevel 16

If assuming (\sqrt{5}=\frac{m}{n}) and squaring gives (m^2=5n^2), what is the correct next form for (m)?

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Answer and explanation

Correct answer: (m=5k)

Step 1: From (m^2=5n^2), (m^2) is divisible by (5). Step 2: Since (5) is prime, (m) is also divisible by (5). Step 3: Therefore (m=5k) is the correct next step.

Tags

sqrt5 proofprime divisibilityclass 10

Frequently asked questions

What is the correct answer to this question?

(m=5k)

Why is this the correct answer?

Step 1: From (m^2=5n^2), (m^2) is divisible by (5). Step 2: Since (5) is prime, (m) is also divisible by (5). Step 3: Therefore (m=5k) is the correct next step.

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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