# proofs

• Mar 26th 2008, 01:09 PM
amiller3
proofs
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, 04:55 AM
CaptainBlack
Quote:

Originally Posted by amiller3
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!!

Suppose that $\sqrt{2}+\sqrt{3}$ is rational, then there exist integers $a$ and $b$
such that:

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

so:

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

squaring:

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

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