Question

(\(\sqrt{5}+1\))\(\sqrt{3-\sqrt{5}}\)

Answer 1

\(\left(\sqrt{5}+1\right)\cdot\sqrt{3-\sqrt{5}}\)

\(=\left(\sqrt{5}+1\right)\cdot\dfrac{\sqrt{6-2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}{\sqrt{2}}=\dfrac{5-1}{\sqrt{2}}=\dfrac{4}{\sqrt{2}}=2\sqrt{2}\)