If (h) is not divisible by (3) and (h^2=3k^2), what inconsistency appears?
Answer and explanation
Correct answer: h^2 must be divisible by 3, which implies that h is also divisible by 3
From h² = 3k², h² is divisible by 3. Since 3 is prime, if it divides the square of an integer, it must also divide that integer. Hence 3 divides h, contradicting the given condition that h is not divisible by 3. Option A is not the required contradiction; the contradiction at this step concerns h directly. Exam tip: For a prime p, use p | n² ⇒ p | n.
Frequently asked questions
What is the correct answer to this question?
h^2 must be divisible by 3, which implies that h is also divisible by 3
Why is this the correct answer?
From h² = 3k², h² is divisible by 3. Since 3 is prime, if it divides the square of an integer, it must also divide that integer. Hence 3 divides h, contradicting the given condition that h is not divisible by 3. Option A is not the required contradiction; the contradiction at this step concerns h directly. Exam tip: For a prime p, use p | n² ⇒ p | 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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