Question

Answer 1

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

2: \(=\sqrt{\left(\sqrt{x}+1\right)^2}=\sqrt{x}+1\)

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

=1+căn x-3

4: \(=\sqrt{x+1-2\sqrt{x+1}+1}=\sqrt{\left(\sqrt{x+1}-1\right)^2}\)

=|căn x+1-1|

6: \(=\sqrt{\left(\sqrt{2x}+1\right)^2}=\sqrt{2x}+1\)

8: \(=\sqrt{x-3+2\sqrt{\left(x+2\right)\left(x-3\right)}+x+2}\)

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