I have to prove the square root of 3 is irrational using proof by contradiction.

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- March 25th 2008, 01:19 PMnatewalker205Contradiction proof
I have to prove the square root of 3 is irrational using proof by contradiction.

- March 25th 2008, 01:38 PMThePerfectHacker
- March 25th 2008, 01:43 PMtopsquark
Say that is not irrational. Then it can be put into the form:

where p and q are integers ( ). For the sake of the argument, let this fraction be in lowest terms.

The we have that

Now, this implies the 3 divides evenly. But we assumed that the fraction is already in lowest terms, so 3 does not divide q. So the prime factorization of only contains a single 3, which is impossible.

Thus etc.

-Dan