Question

Answer 1

1: \(\sqrt{\left(4-\sqrt{9}\right)^2}=\sqrt{\left(4-3\right)^2}=\sqrt{1^2}=1\)

2: \(\sqrt{\left(4-\sqrt{6}\right)^2}=\left|4-\sqrt{6}\right|=4-\sqrt{6}\)

3: \(\sqrt{\left(3-\sqrt{11}\right)^2}=\left|3-\sqrt{11}\right|=\sqrt{11}-3\)

4: \(\sqrt{\left(2\sqrt{2}-3\right)^2}=\left|2\sqrt{2}-3\right|=3-2\sqrt{2}\)

5: \(\sqrt{\left(10-\sqrt{10}\right)^2}=\left|10-\sqrt{10}\right|=10-\sqrt{10}\)

6: \(\sqrt{\left(\sqrt{3}-2\right)^2}=\left|\sqrt{3}-2\right|=2-\sqrt{3}\)

7: \(\sqrt{\left(1+\sqrt{3}\right)^2}=\left|1+\sqrt{3}\right|=\sqrt{3}+1\)

8: \(\sqrt{\left(\sqrt{3}-3\right)^2}=\left|\sqrt{3}-3\right|=3-\sqrt{3}\)

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

10: \(\sqrt{\left(3-\sqrt{8}\right)^2}=\left|3-\sqrt{8}\right|=3-\sqrt{8}=3-2\sqrt{2}\)

11: \(\sqrt{\left(\sqrt{2}-1\right)^2}=\left|\sqrt{2}-1\right|=\sqrt{2}-1\)

12: \(\sqrt{\left(3+\sqrt{8}\right)^2}=\left|3+\sqrt{8}\right|=3+2\sqrt{2}\)