How to simplify $\sqrt{\sqrt{5}+1} \cdot \sqrt{\sqrt{5}-1}$? This is the original problem:
$\sqrt{\sqrt{5}+1} \cdot \sqrt{\sqrt{5}-1} = x$.
I'm really confused about how to solve this problem, I come as far as saying this: $\sqrt[4]{5} + \sqrt{1}\cdot \sqrt[4]{5}-\sqrt{1}$.

$$\sqrt{\sqrt{5}+1}\sqrt{\sqrt{5}-1}=\sqrt{(\sqrt{5}+1)(\sqrt{5}-1)}$$ $$=\sqrt{5-\sqrt{5}+\sqrt{5}-1}$$ $$=\sqrt{5-1}$$ $$=\sqrt{4}$$ $$=2$$
