(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that [tex]\sqrt{2}+\sqrt{3}[/tex] is irrational.

2. Relevant equations

3. The attempt at a solution

So we know that [tex](\sqrt{2}+\sqrt{3})(\sqrt{3}-\sqrt{2}) = 1[/tex]. But a rational number must be of the form a/b, and if (a/b)c = 1, the only number c that works (for rational numbers) is c = b/a in reduced form due to unique inverses for rational numbers. But here we have a value of c that is NOT of the form c = b/a. And so once we prove that [tex]\sqrt{2}+\sqrt{3}[/tex] is NOT [tex]\frac{1}{\sqrt{3}-\sqrt{2}}[/tex], we can only conclude that [tex](\sqrt{2}+\sqrt{3})[/tex] is irrational.

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# Homework Help: Does this proof for irrationality of sqrt(2)+sqrt(3) work?

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