Which is the correct short order of the proof that √2 is irrational?
Answer and explanation
Correct answer: Assume it rational, square the equation, then derive that both integers are even
The governing concept is an indirect proof of irrationality. First suppose, contrary to what is to be proved, that √2 is rational. Write √2 = m/n in lowest form, where m and n are integers, n is nonzero, and they are coprime. Squaring gives m² = 2n². This shows m is even; writing m = 2k and substituting then shows n is also even. That conclusion contradicts the lowest-form assumption, because m and n would share the factor 2. Hence the assumption is false and √2 is irrational. Option A gives this correct order. A decimal calculation is not the rigorous proof, and drawing or assuming zero has no role in the argument.
Frequently asked questions
What is the correct answer to this question?
Assume it rational, square the equation, then derive that both integers are even
Why is this the correct answer?
The governing concept is an indirect proof of irrationality. First suppose, contrary to what is to be proved, that √2 is rational. Write √2 = m/n in lowest form, where m and n are integers, n is nonzero, and they are coprime. Squaring gives m² = 2n². This shows m is even; writing m = 2k and substituting then shows n is also even. That conclusion contradicts the lowest-form assumption, because m and n would share the factor 2. Hence the assumption is false and √2 is irrational. Option A gives this correct order. A decimal calculation is not the rigorous proof, and drawing or assuming zero has no role in the argument.
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.
