Question

[~Tiểu Hoa Hoa~]

1) \(\left(\sqrt{6}-\sqrt{8}\right)\left(\sqrt{6}+\sqrt{8}\right).\)

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

3)\(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)

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

5)\(\sqrt{4\sqrt{6}+11}-\sqrt{11-4\sqrt{6}}\)

6)\(\sqrt{10+2\sqrt{11}}-\sqrt{10-2\sqrt{11}}\)

7)\(\sqrt{5-2\sqrt{7-2\sqrt{6}}}\)

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Answer 1

[Nguyễn Minh Đăng]

1) \(\left(\sqrt{6}-\sqrt{8}\right)\left(\sqrt{6}+\sqrt{8}\right)\)

\(=\left(\sqrt{6}\right)^2-\left(\sqrt{8}\right)^2\)

\(=6-8=-2\)

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

\(=3^2-\left(\sqrt{5}\right)^2\)

\(=9-5=4\)

Answer 2

[Nguyễn Minh Đăng]

3) \(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)

\(=\sqrt{4-4\sqrt{3}+3}+\sqrt{4+4\sqrt{3}+3}\)

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

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

4) Xét ta thấy: \(2\sqrt{3}=\sqrt{12}< \sqrt{16}=4\)

=> \(2\sqrt{3}-4< 0\) => vô lý không tm đk căn