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In the proof for (\sqrt{2}), if someone writes (q^2=4k^2) after putting (p=2k), what is the correct correction?
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Answer and explanation
Correct answer: It should be (q^2=2k^2)
Step 1: Substituting (p=2k) in (p^2=2q^2) gives (4k^2=2q^2). Step 2: Dividing both sides by (2) gives (q^2=2k^2). Step 3: Reduce factors carefully during algebraic simplification.
Frequently asked questions
What is the correct answer to this question?
It should be (q^2=2k^2)
Why is this the correct answer?
Step 1: Substituting (p=2k) in (p^2=2q^2) gives (4k^2=2q^2). Step 2: Dividing both sides by (2) gives (q^2=2k^2). Step 3: Reduce factors carefully during algebraic simplification.
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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