From (q^2=3r^2) what conclusion is obtained about (q)?
Answer and explanation
Correct answer: q is divisible by 3
Given q² = 3r², q² is divisible by 3. Since 3 is prime, if 3 divides the square of an integer, it must also divide the integer itself. Therefore, q is divisible by 3. Divisibility of q² by 3 does not imply that q is even or zero. Exam tip: For a prime p, use p | a² ⇒ p | a.
Frequently asked questions
What is the correct answer to this question?
q is divisible by 3
Why is this the correct answer?
Given q² = 3r², q² is divisible by 3. Since 3 is prime, if 3 divides the square of an integer, it must also divide the integer itself. Therefore, q is divisible by 3. Divisibility of q² by 3 does not imply that q is even or zero. Exam tip: For a prime p, use p | a² ⇒ p | a.
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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