3) \(\sqrt{\left(\sqrt{5}-3\right)^2}-\sqrt{\left(2+\sqrt{5}\right)^2}\)
\(=\left|\sqrt{5}-3\right|-\left|2+\sqrt{5}\right|\)
\(=3-\sqrt{5}-2-\sqrt{5}\)
\(=1-2\sqrt{5}\)
4) \(\sqrt{\left(4-\sqrt{17}\right)^2}-\sqrt{\left(\sqrt{17}-3\right)^2}\)
\(=\left|4-\sqrt{17}\right|-\left|\sqrt{17}-3\right|\)
\(=\sqrt{17}-4-\sqrt{17}+3\)
\(=-1\)
5) \(\sqrt{\left(5-\sqrt{6}\right)^2}-\sqrt{\left(2-\sqrt{6}\right)^2}\)
\(=\left|5-\sqrt{6}\right|-\left|2-\sqrt{6}\right|\)
\(=5-\sqrt{6}-\sqrt{6}+2\)
\(=7-2\sqrt{6}\)
6) \(\sqrt{\left(17+\sqrt{47}\right)^2}-\sqrt{\left(7-\sqrt{47}\right)^2}\)
\(=\left|17+\sqrt{47}\right|-\left|7-\sqrt{47}\right|\)
\(=17+\sqrt{47}-7-\sqrt{47}\)
\(=10+2\sqrt{47}\)
