Which option clearly shows that assuming (\sqrt{5}) rational is wrong?
Answer and explanation
Correct answer: Numerator and denominator in lowest form both turn out divisible by (5)
Step 1: Assuming rationality, (\sqrt{5}=\frac{a}{b}) is taken in lowest form. Step 2: The proof shows that both (a) and (b) are divisible by (5). Step 3: This cannot happen in lowest form, so the assumption is false.
Frequently asked questions
What is the correct answer to this question?
Numerator and denominator in lowest form both turn out divisible by (5)
Why is this the correct answer?
Step 1: Assuming rationality, (\sqrt{5}=\frac{a}{b}) is taken in lowest form. Step 2: The proof shows that both (a) and (b) are divisible by (5). Step 3: This cannot happen in lowest form, so the assumption is false.
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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