CSE 215 Lecture 13: Classic Theorems
9 Mar 2017
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Show that the square root of 2 is irrational. We will assume that the square root of 2 is rational. In this case, sqrt(2) = a/b for some integers a and b. We can also assume that a and b don"t have any common divisors (because if they did, then we can remove them for each term and get a ratio of smaller numbers. This would give us with wo different numbers instead. ) The line above gives us that a2 is even since we can write it in the form 2k for some integer k. This also means that a is also even since the squareroot of an even square is also even. That means we can let a represent an even number where a = 2k for some integer k. From equation 1, we can rewrite it into 4k2 = 2b2. This shows that b2 is even since we can write it in the form of an even number.
