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If assuming (\sqrt{3}) rational gives (p^2=3q^2), which is the correct chain until (q) is proved divisible by (3)?
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Answer and explanation
Correct answer: (p^2=3q^2), (p=3k), (9k^2=3q^2), (q^2=3k^2)
Step 1: From (p^2=3q^2), (p) is divisible by (3), so (p=3k). Step 2: Substitution gives (9k^2=3q^2), then (q^2=3k^2). Step 3: This proves (q) is also divisible by (3).
Frequently asked questions
What is the correct answer to this question?
(p^2=3q^2), (p=3k), (9k^2=3q^2), (q^2=3k^2)
Why is this the correct answer?
Step 1: From (p^2=3q^2), (p) is divisible by (3), so (p=3k). Step 2: Substitution gives (9k^2=3q^2), then (q^2=3k^2). Step 3: This proves (q) is also divisible by (3).
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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