Question

[Trần Thị Thùy Luyến]

Tính

1. \(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}\)

2. \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

3. \(\left(\sqrt{2}-\sqrt{9}\right)\left(\sqrt{11+2\sqrt{18}}\right)\)

4. \(\left(\sqrt{5}+\sqrt{7}\right)\left(\sqrt{12-2\sqrt{35}}\right)\)

Answer 1

[Trần Đức Thắng]

   1,\(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(2\sqrt{6}-3\right)^2}=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

   2, (tương tự ý 1 cũng tách thành hằng đẳng thức \(\sqrt{46-6\sqrt{5}}=\sqrt{\left(3\sqrt{5}-1\right)^2}\)và \(\sqrt{29-12\sqrt{5}}=\sqrt{\left(2\sqrt{5}-3\right)^2}\)

    3,\(\left(\sqrt{2}-\sqrt{9}\right)\left(\sqrt{\left(3+\sqrt{2}\right)^2}\right)=\left(\sqrt{2}-3\right)\left(\sqrt{2}+3\right)=2-9=-7\)

4, tương tự ý 3