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In the proof for (\sqrt{3}), if someone writes (a=3b) directly from (3\mid a^2), what is the mistake?
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Answer and explanation
Correct answer: We get that (a) is divisible by (3), but (a=3b) is not necessary
Step 1: From (3\mid a^2), we get (3\mid a). Step 2: So (a=3k) is correct, where (k) is an integer; it is not necessary that (k=b). Step 3: Using a new helper variable is safer.
Frequently asked questions
What is the correct answer to this question?
We get that (a) is divisible by (3), but (a=3b) is not necessary
Why is this the correct answer?
Step 1: From (3\mid a^2), we get (3\mid a). Step 2: So (a=3k) is correct, where (k) is an integer; it is not necessary that (k=b). Step 3: Using a new helper variable is safer.
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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