Question

Answer 1

1: \(=\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}=\sqrt{3}\)

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

3: \(=\dfrac{\left(\sqrt{2}+1-\sqrt{2}+1\right)}{\sqrt{2}-1}=\dfrac{2}{\sqrt{2}-1}=2\sqrt{2}+2\)

5: \(=\dfrac{8+2\sqrt{15}+8-2\sqrt{15}}{2}=\dfrac{16}{2}=8\)

6: \(=\dfrac{6-2\sqrt{5}-6-2\sqrt{5}}{4}=-\sqrt{5}\)