If assuming √3 is rational breaks the coprime condition, which conclusion is correct?
Answer and explanation
Correct answer: √3 is irrational
For a contradiction proof, suppose √3 = m/n in lowest terms. Squaring gives m² = 3n², so the prime-factor rule implies that 3 divides m. Substituting m = 3k then shows that 3 also divides n, contradicting that m and n are coprime. Hence the rational assumption is impossible and √3 is irrational, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
√3 is irrational
Why is this the correct answer?
For a contradiction proof, suppose √3 = m/n in lowest terms. Squaring gives m² = 3n², so the prime-factor rule implies that 3 divides m. Substituting m = 3k then shows that 3 also divides n, contradicting that m and n are coprime. Hence the rational assumption is impossible and √3 is irrational, so option B is correct.
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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