Use the fact that sqrt2 is irrational to prove that sqrt2 + sqrt3 is irrational

...im not sure if I'm posting this right...i dont know how to put the sqrt symbol up. but any help would be much appreciated!!

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- Mar 26th 2008, 12:09 PMamiller3proofs
Use the fact that sqrt2 is irrational to prove that sqrt2 + sqrt3 is irrational

...im not sure if I'm posting this right...i dont know how to put the sqrt symbol up. but any help would be much appreciated!! - Mar 27th 2008, 03:55 AMCaptainBlack
Suppose that $\displaystyle \sqrt{2}+\sqrt{3}$ is rational, then there exist integers $\displaystyle a$ and $\displaystyle b$

such that:

$\displaystyle \sqrt{2}+\sqrt{3}=\frac{a}{b}$

so:

$\displaystyle \sqrt{3}=\frac{a}{b}-\sqrt{2}$

squaring:

$\displaystyle 3=\frac{a^2}{b^2}-2\frac{a}{b}\sqrt{2}+2$

from this point it should be simple, so I will leave you to complete the proof

by contradiction.

RonL