From (b^2=3k^2), what conclusion follows about (b)?
Answer and explanation
Correct answer: b is divisible by 3
The equation \(b^2=3k^2\) shows that \(b^2\) is divisible by 3. Since 3 is prime, if it divides the square of an integer, it must also divide the integer itself. Therefore, \(b\) is divisible by 3. Divisibility of \(b\) by 2 does not follow from this equation. Exam tip: Remember that for a prime \(p\), \(p\mid n^2\Rightarrow p\mid n\).
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What is the correct answer to this question?
b is divisible by 3
Why is this the correct answer?
The equation \(b^2=3k^2\) shows that \(b^2\) is divisible by 3. Since 3 is prime, if it divides the square of an integer, it must also divide the integer itself. Therefore, \(b\) is divisible by 3. Divisibility of \(b\) by 2 does not follow from this equation. Exam tip: Remember that for a prime \(p\), \(p\mid n^2\Rightarrow p\mid n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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