Which option gives the correct order of proof for the irrationality of (\sqrt{5})?
Answer and explanation
Correct answer: Assume (\sqrt{5}=\frac{a}{b}), then (a^2=5b^2), then (5\mid a), then (5\mid b)
Step 1: The correct proof starts by assuming the number is rational. Step 2: Squaring gives (a^2=5b^2), and divisibility by (5) is then forced on both variables. Step 3: Keeping the order correct makes the proof clear.
Frequently asked questions
What is the correct answer to this question?
Assume (\sqrt{5}=\frac{a}{b}), then (a^2=5b^2), then (5\mid a), then (5\mid b)
Why is this the correct answer?
Step 1: The correct proof starts by assuming the number is rational. Step 2: Squaring gives (a^2=5b^2), and divisibility by (5) is then forced on both variables. Step 3: Keeping the order correct makes the proof clear.
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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