Question

Answer 1

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

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

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

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

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

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

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

8) \(\sqrt{\left(4-\sqrt{17}\right)^2}=\sqrt{17}-4\)

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

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

Answer 2

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

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

3. \(\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)

4. \(\sqrt{\left(\sqrt{3}+2\right)^2}=\left|\sqrt{3}+2\right|=\sqrt{3}+2\)

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

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

7. \(\sqrt{\left(3-\sqrt{7}\right)^2}=\left|3-\sqrt{7}\right|=3-\sqrt{7}\)

8. \(\sqrt{\left(4-\sqrt{17}\right)^2}=\left|4-\sqrt{17}\right|=\sqrt{17}-4\)

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

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