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If in the proof of (\sqrt{3}), both (p) and (q) turn out divisible by (3), which greatest common divisor condition definitely breaks?
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Answer and explanation
Correct answer: (\gcd(p,q)=1)
Step 1: Taking (\frac{p}{q}) in lowest form means (\gcd(p,q)=1). Step 2: If both are divisible by (3), their greatest common divisor is at least (3). Step 3: Therefore the condition (\gcd(p,q)=1) breaks.
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What is the correct answer to this question?
(\gcd(p,q)=1)
Why is this the correct answer?
Step 1: Taking (\frac{p}{q}) in lowest form means (\gcd(p,q)=1). Step 2: If both are divisible by (3), their greatest common divisor is at least (3). Step 3: Therefore the condition (\gcd(p,q)=1) breaks.
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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