Which option shows the correct logical chain in the proof of (√2)?
Answer and explanation
Correct answer: (m²=2n²), (m) even, (m=2r), (n) even
To prove √2 irrational, assume √2 = m/n, where m and n are coprime integers and n is non-zero. Squaring gives m² = 2n². The right side is even, so m² is even; consequently m is even. Write m = 2r. Substitution gives 4r² = 2n², hence n² = 2r², so n is also even. Thus m and n share a factor 2, contradicting the assumption that the fraction was in lowest terms. Option A presents this essential chain. Option B belongs to the analogous √3 argument, while C and D omit or contradict the required reasoning.
Frequently asked questions
What is the correct answer to this question?
(m²=2n²), (m) even, (m=2r), (n) even
Why is this the correct answer?
To prove √2 irrational, assume √2 = m/n, where m and n are coprime integers and n is non-zero. Squaring gives m² = 2n². The right side is even, so m² is even; consequently m is even. Write m = 2r. Substitution gives 4r² = 2n², hence n² = 2r², so n is also even. Thus m and n share a factor 2, contradicting the assumption that the fraction was in lowest terms. Option A presents this essential chain. Option B belongs to the analogous √3 argument, while C and D omit or contradict the required reasoning.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
