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 $\displaystyle \sqrt{2}+\sqrt{3}$ 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