Question

[Qúy Công Tử]

Tính

1) \(\sqrt{9-4\sqrt{5}}\)

2) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)

3) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)

4) \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)

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

6) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

1: \(=\sqrt{5}-2\)

2: \(=2\sqrt{3}+4\sqrt{3}-5\sqrt{3}-9\sqrt{3}=-8\sqrt{3}\)

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

5: \(=\dfrac{8-2\sqrt{15}+8+2\sqrt{15}}{2}-\dfrac{6+2\sqrt{5}}{4}\)

\(=\dfrac{16-\sqrt{5}-1}{2}=\dfrac{15-\sqrt{5}}{2}\)