Which option best expresses the main idea behind the irrationality of (\sqrt{2})?
Answer and explanation
Correct answer: Assuming rationality makes numerator and denominator of the lowest fraction both even
Step 1: (\sqrt{2}) is assumed rational and written as a fraction in lowest form. Step 2: The proof shows that numerator and denominator are both even. Step 3: This is impossible in lowest form, so (\sqrt{2}) is irrational.
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What is the correct answer to this question?
Assuming rationality makes numerator and denominator of the lowest fraction both even
Why is this the correct answer?
Step 1: (\sqrt{2}) is assumed rational and written as a fraction in lowest form. Step 2: The proof shows that numerator and denominator are both even. Step 3: This is impossible in lowest form, so (\sqrt{2}) 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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