Which method is used in the proof of the irrationality of √2?
Answer and explanation
Correct answer: Contradiction method
The proof uses the method of contradiction, also called proof by contradiction or reductio ad absurdum. First, the opposite of the desired statement is assumed: √2 is taken to be rational and written as p/q in lowest form. Algebraic manipulation then shows that p and q must both be even. This is impossible because a fraction in lowest form cannot have a common factor greater than 1. The impossible conclusion contradicts the original assumption, so the assumption that √2 is rational must be false. Therefore √2 is irrational, and option B correctly names the method. Measurement, guessing, and drawing are not the logical proof procedures used here.
Frequently asked questions
What is the correct answer to this question?
Contradiction method
Why is this the correct answer?
The proof uses the method of contradiction, also called proof by contradiction or reductio ad absurdum. First, the opposite of the desired statement is assumed: √2 is taken to be rational and written as p/q in lowest form. Algebraic manipulation then shows that p and q must both be even. This is impossible because a fraction in lowest form cannot have a common factor greater than 1. The impossible conclusion contradicts the original assumption, so the assumption that √2 is rational must be false. Therefore √2 is irrational, and option B correctly names the method. Measurement, guessing, and drawing are not the logical proof procedures used here.
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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