In the proof of (\sqrt{5}), if both (p) and (q) are proved divisible by (5), which conclusion is the most logical?
Answer and explanation
Correct answer: (\frac{p}{q}) was not in lowest form, so the rational assumption is impossible
Step 1: If both are divisible by (5), numerator and denominator have common factor (5). Step 2: Such a situation cannot occur in lowest form. Step 3: Therefore the rational assumption is impossible and (\sqrt{5}) is irrational.
Frequently asked questions
What is the correct answer to this question?
(\frac{p}{q}) was not in lowest form, so the rational assumption is impossible
Why is this the correct answer?
Step 1: If both are divisible by (5), numerator and denominator have common factor (5). Step 2: Such a situation cannot occur in lowest form. Step 3: Therefore the rational assumption is impossible and (\sqrt{5}) is irrational.
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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