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In the proof of irrationality of (\sqrt{5}), why does (a^2=5b^2) imply that (a) is divisible by (5)?
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Answer and explanation
Correct answer: Because (5) is prime and (5\mid a^2)
Step 1: From (a^2=5b^2), (a^2) clearly has (5) as a factor. Step 2: Since (5) is prime, (a) must also have (5) as a factor. Step 3: Apply the prime-factor rule carefully.
Frequently asked questions
What is the correct answer to this question?
Because (5) is prime and (5\mid a^2)
Why is this the correct answer?
Step 1: From (a^2=5b^2), (a^2) clearly has (5) as a factor. Step 2: Since (5) is prime, (a) must also have (5) as a factor. Step 3: Apply the prime-factor rule carefully.
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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