\(13,\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(=\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}.\sqrt{5}+\sqrt{5^2}}+\sqrt{\left(2\sqrt{2}\right)^2-2.2\sqrt{2}.\sqrt{5}+\sqrt{5^2}}\)
\(=\sqrt{\left(2\sqrt{2}+\sqrt{5}\right)^2}+\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)
\(=\left|2\sqrt{2}+\sqrt{5}\right|+\left|2\sqrt{2}-\sqrt{5}\right|\)
\(=2\sqrt{2}+\sqrt{5}+2\sqrt{2}-\sqrt{5}\)
\(=2\sqrt{2}+2\sqrt{2}+0\)
\(=4\sqrt{2}\)
14: \(=\dfrac{1}{\sqrt{2}}\cdot\sqrt{4-2\sqrt{3}}=\dfrac{1}{\sqrt{2}}\left(\sqrt{3}-1\right)=\dfrac{\sqrt{6}-\sqrt{2}}{2}\)
12: \(=3-\sqrt{5}-3-\sqrt{5}=-2\sqrt{5}\)
13:
\(=2\sqrt{2}+\sqrt{5}+2\sqrt{2}-\sqrt{5}=4\sqrt{2}\)
9: \(=\left(\sqrt{2}-3\right)\left(3+\sqrt{2}\right)=-9+2=-7\)
4: \(=\left|\sqrt{5}+\sqrt{3}\right|=\sqrt{5}+\sqrt{3}\)
5: \(=\left|\sqrt{7}-\sqrt{5}\right|=\sqrt{7}-\sqrt{5}\)
1: \(=\left|\sqrt{2}+1\right|=\sqrt{2}+1\)
2: \(=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)
