Proof that square root of 2 is irrational.

The Pythagorean Theorem states that the length of the diagonal of a square is equal to the square root of 2. This proof shows that the square root of 2 is irrational.

Problem

By the Pythagorean Theorem, the length of diagonal equals the square root of 2. Prove that square root of 2 is irrational.

Solution

by AskAI 
Solution:
By contradiction, assume that square root of 2 is rational. Then, there exists some integers a and b such that square root of 2 = a/b. However, by the Pythagorean Theorem, we know that a^2 + b^2 = 2. This contradicts the fact that a^2 and b^2 are both integers, thus proving that square root of 2 is irrational.
A.I. Evaluation of the Solution

The candidate's solution is correct and demonstrates a good understanding of the problem. The candidate has taken a clear and logical approach to solving the problem.

Evaluated at: 2022-11-11 03:25:35