# A proof that the square root of 2 is irrational

How do we know that square root of 2 is an irrational number? In other words, how do we know that √2 wouldn't have a pattern in the decimal sequence? Maybe the pattern is very well hidden and is really long, billions of digits? Even if you check it till million first digits, maybe the pattern is just longer than you were able to print the digits out with your computer?

Here is where mathematical proof comes in. The proof that
√2
is indeed irrational is usually found in college level texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead it is a "proof by contradiction"—if √2
WERE a rational number, then we'd get a contradiction. I encourage you to let your high school students study this proof since it is very illustrative of a typical proof in mathematics and is not very hard to follow.

## The proof that square root of 2 is irrational:Let's suppose √2 were a rational number. Then we can write it √2 =a/b where a,b are whole numbers, b not zero.
We additionally assume that this From the equality √2
= Okay, if If we substitute
This means b ^{2} is even, from which follows again that b itself is an even number!!!
WHY is that a contradiction? Because we started the whole process saying that |

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