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In the proof of (\sqrt{2}), after putting (p=2r), which correct simplification is obtained from (p^2=2q^2)?
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Answer and explanation
Correct answer: (q^2=2r^2)
Step 1: If (p=2r), then (p^2=4r^2). Step 2: From (4r^2=2q^2), dividing both sides by (2) gives (q^2=2r^2). Step 3: This proves (q^2), and then (q), is even.
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What is the correct answer to this question?
(q^2=2r^2)
Why is this the correct answer?
Step 1: If (p=2r), then (p^2=4r^2). Step 2: From (4r^2=2q^2), dividing both sides by (2) gives (q^2=2r^2). Step 3: This proves (q^2), and then (q), is even.
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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