1. ## Prove Q(\sqrt{2}+\sqrt{3})=Q(\sqrt{2},\sqrt{3})

Prove Q( +)=Q(,)

2. Originally Posted by apple2009
Prove Q( +)=Q(,)
let $\displaystyle \alpha=\sqrt{2}+\sqrt{3}.$ then $\displaystyle \frac{1}{\alpha}=\sqrt{3}-\sqrt{2}$ and thus $\displaystyle \sqrt{3}=\frac{\alpha^2+1}{2\alpha} \in \mathbb{Q}(\alpha)$ and $\displaystyle \sqrt{2}=\alpha - \sqrt{3} \in \mathbb{Q}(\alpha).$

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# show that q(sqrt 2 sqrt 3)=q(sqrt 2 sqrt 3)

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