If someone writes (p=3q) from (p^2=3q^2), what is the correct correction?
Answer and explanation
Correct answer: 3 p को विभाजित करता है, इसलिए p=3k (जहाँ k एक पूर्णांक है) लिखना चाहिए; फिर प्रतिस्थापन से q भी 3 से विभाज्य होगा
Since \(p^2=3q^2\), \(p^2\) is divisible by 3. As 3 is prime, if \(p^2\) is divisible by 3, then \(p\) must also be divisible by 3. Hence, write \(p=3r\), where \(r\) is an integer. Writing \(p=3q\) is unjustified because it incorrectly makes \(p\) directly three times \(q\). Exam tip: when a square is divisible by a prime, first conclude that its base is divisible by that prime.
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What is the correct answer to this question?
3 p को विभाजित करता है, इसलिए p=3k (जहाँ k एक पूर्णांक है) लिखना चाहिए; फिर प्रतिस्थापन से q भी 3 से विभाज्य होगा
Why is this the correct answer?
Since \(p^2=3q^2\), \(p^2\) is divisible by 3. As 3 is prime, if \(p^2\) is divisible by 3, then \(p\) must also be divisible by 3. Hence, write \(p=3r\), where \(r\) is an integer. Writing \(p=3q\) is unjustified because it incorrectly makes \(p\) directly three times \(q\). Exam tip: when a square is divisible by a prime, first conclude that its base is divisible by that prime.
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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