Prove that root 2 + root 3 is irrational.

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Here is another proof which is conceptually interesting.
Now √ 3 + √ 2 and √ 3 - √ 2 are either both rational or both irrational for their product is 1.
If they are both rational then their difference would be rational too.
But their difference is 2√ 2 which we know to be irrational.
Hence √ 3 + √ 2 and √ 3 - √ 2 are both irrational.
This method also shows that if √ p and √ q are irrational then
their sum and difference are also irrational

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