Question

[Trang Nguyễn Thu]

1. A=\(\sqrt{4+\sqrt{ }7}\)+ \(\sqrt{4-\sqrt{ }7}\) 2. B=\(\dfrac{\sqrt{\sqrt{7-\sqrt{3}}}-\sqrt{\sqrt{7+\sqrt{3}}}}{\sqrt{\sqrt{7}-\sqrt{2}}}\) 3. C=\(\sqrt{6+2\sqrt{2\cdot\sqrt{3-\sqrt{4+2\sqrt{3}}}}}\) 4. D=\(\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\) 5. so sánh Cho A=\(\sqrt{11+\sqrt{96}}\) B=\(\dfrac{2\sqrt{2}}{\sqrt{1+\sqrt{2-\sqrt{3}}}}\) so sánh A và B

Answer 1

[Nguyễn Lê Phước Thịnh]

1: \(=\dfrac{\sqrt{8+2\sqrt{7}}+\sqrt{8-2\sqrt{7}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7}+1+\sqrt{7}-1}{\sqrt{2}}=\dfrac{2\sqrt{7}}{\sqrt{2}}=\sqrt{14}\)

3: \(=\sqrt{6+2\sqrt{2\cdot\sqrt{3-\sqrt{3}-1}}}\)

\(=\sqrt{6+2\sqrt{2\cdot\sqrt{2-\sqrt{3}}}}\)

\(=\sqrt{6+2\sqrt{\sqrt{2}\left(\sqrt{3}-1\right)}}\)

\(=\sqrt{6+2\sqrt{\sqrt{6}-\sqrt{2}}}\)