Which statement gives both the correct conclusion and reason in the proof of (\sqrt{5})?
Answer and explanation
Correct answer: (\sqrt{5}) is irrational because assuming rational makes both (p) and (q) divisible by (5)
Step 1: Assuming (\sqrt{5}) rational gives (p^2=5q^2). Step 2: This proves both (p) and (q) divisible by (5). Step 3: This contradicts coprime condition, so (\sqrt{5}) is irrational.
Frequently asked questions
What is the correct answer to this question?
(\sqrt{5}) is irrational because assuming rational makes both (p) and (q) divisible by (5)
Why is this the correct answer?
Step 1: Assuming (\sqrt{5}) rational gives (p^2=5q^2). Step 2: This proves both (p) and (q) divisible by (5). Step 3: This contradicts coprime condition, so (\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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