If (r^2=3s^2), what is true about (r^2)?
Answer and explanation
Correct answer: \(r^2\) is divisible by 3
Given \(r^2=3s^2\). For integers, \(s^2\) is an integer, so \(r^2\) is the product of 3 and the integer \(s^2\). Hence, \(r^2\) is divisible by 3. The equation does not necessarily imply that \(r^2\) is divisible by 2. Exam tip: To prove divisibility by \(k\), express the number as \(k\times\) an integer.
Frequently asked questions
What is the correct answer to this question?
\(r^2\) is divisible by 3
Why is this the correct answer?
Given \(r^2=3s^2\). For integers, \(s^2\) is an integer, so \(r^2\) is the product of 3 and the integer \(s^2\). Hence, \(r^2\) is divisible by 3. The equation does not necessarily imply that \(r^2\) is divisible by 2. Exam tip: To prove divisibility by \(k\), express the number as \(k\times\) an integer.
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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