Prove that √2 is irrational.

Solution

If √2 IS rational, then for some integers a and b √2 = a / b, and
the fraction can not be reduced.
Hence a * a = 2 * b * b => a * a is even => a is even.
Hence a can be represented as 2 * k.
Hence a * a is equal to 4 * k * k => 2 * k * k = b * b =>
=> b * b is even => b is even too => both a and b are even =>
a / b CAN BE reduced => oops, we have a contradiction!

Add square root of 2
Add square root of 2
