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In the proof of (\sqrt{2}), if (p=2k) and (q=2r), how can (\frac{p}{q}) be reduced?
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Answer and explanation
Correct answer: (\frac{p}{q}=\frac{2k}{2r}=\frac{k}{r})
Step 1: If (p=2k) and (q=2r), both numerator and denominator have common factor (2). Step 2: So (\frac{2k}{2r}) can be reduced to (\frac{k}{r}). Step 3: This shows (\frac{p}{q}) was not in lowest form.
Frequently asked questions
What is the correct answer to this question?
(\frac{p}{q}=\frac{2k}{2r}=\frac{k}{r})
Why is this the correct answer?
Step 1: If (p=2k) and (q=2r), both numerator and denominator have common factor (2). Step 2: So (\frac{2k}{2r}) can be reduced to (\frac{k}{r}). Step 3: This shows (\frac{p}{q}) was not in lowest form.
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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