Question

Prove that√2 is an irrational number.​

Answer 1

Answer:

The proof that √2 is indeed irrational is usually found in college level math texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead is a "proof by contradiction": if √2 WERE a rational number, we'd get a contradiction.

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A proof that the square root of 2 is irrational.

2 = (2k)2/b2

2*b2 = 4k2

b2 = 2k2

Answer 2

If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:

2 = (2k)2/b2

2 = 4k2/b2

2*b2 = 4k2

b2 = 2k2

This means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!