Question

Answer 1

2:

1: \(=\sqrt{18-2\cdot3\sqrt{2}\cdot1+1}=\sqrt{\left(3\sqrt{2}-1\right)^2}=3\sqrt{2}-1\)

2: \(=\sqrt{7-2\cdot\sqrt{7}\cdot2+4}=\sqrt{\left(\sqrt{7}-2\right)^2}=\sqrt{7}-2\)

3: \(=\sqrt{9+2\cdot3\cdot\sqrt{2}+2}=\sqrt{\left(3+\sqrt{2}\right)^2}=3+\sqrt{2}\)

4: \(=\sqrt{11-2\cdot\sqrt{11}\cdot\sqrt{3}+3}=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\sqrt{11}-\sqrt{3}\)

5: \(=\sqrt{9+2\cdot3\cdot\sqrt{2}+2}=\sqrt{\left(3+\sqrt{2}\right)^2}=3+\sqrt{2}\)

6: \(=\sqrt{9+2\cdot3\cdot\sqrt{6}+6}=\sqrt{\left(3+\sqrt{6}\right)^2}=3+\sqrt{6}\)

7: \(=\sqrt{7-2\cdot\sqrt{7}\cdot2+4}=\sqrt{\left(\sqrt{7}-2\right)^2}=\sqrt{7}-2\)