# Math Help - proofs

1. ## 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!!

2. 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