From (a^2=3b^2), which conclusion is obtained about (a^2)?
Answer and explanation
Correct answer: \(a^2\) is divisible by 3
Given \(a^2=3b^2\). Since \(3b^2\) is a multiple of 3, the equal quantity \(a^2\) must also be divisible by 3. The equation does not imply that \(a^2\) must be divisible by 2. Exam tip: if a number can be written as \(3\times\) an integer, it is divisible by 3.
Frequently asked questions
What is the correct answer to this question?
\(a^2\) is divisible by 3
Why is this the correct answer?
Given \(a^2=3b^2\). Since \(3b^2\) is a multiple of 3, the equal quantity \(a^2\) must also be divisible by 3. The equation does not imply that \(a^2\) must be divisible by 2. Exam tip: if a number can be written as \(3\times\) an integer, it is divisible by 3.
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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