1: \(\sqrt{\left.\left(3-2\sqrt2\right)^2\right.}+\sqrt{\left(4-2\sqrt2\right)^2}\)
\(=3-2\sqrt2+4-2\sqrt2\)
\(=7-4\sqrt2\)
2: Ta có: \(\sqrt{6+2\sqrt5}-\sqrt{6-2\sqrt5}\)
\(=\sqrt{\left(\sqrt5+1\right)^2}-\sqrt{\left.\left(\sqrt5-1\right)^2\right.}\)
\(=\sqrt5+1-\sqrt5+1=1+1=2\)
3: \(\sqrt{14+6\sqrt5}+\sqrt{14-6\sqrt5}\)
\(=\sqrt{\left(3+\sqrt5\right)^2}+\sqrt{\left(3-\sqrt5\right)^2}\)
\(=3+\sqrt5+3-\sqrt5=6\)
4: \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
\(=\sqrt{\left(\sqrt5-\sqrt2\right)^2}-\sqrt{\left(\sqrt5+\sqrt2\right)^2}\)
\(=\sqrt5-\sqrt2-\sqrt5-\sqrt2=-2\sqrt2\)
5: \(\sqrt{11-6\sqrt2}+\sqrt{27-18\sqrt2}\)
\(=\sqrt{\left(3-\sqrt2\right)^2}+3\cdot\sqrt{3-2\sqrt2}\)
\(=3-\sqrt2+3\cdot\sqrt{\left(\sqrt2-1\right)^2}\)
\(=3-\sqrt2+3\left(\sqrt2-1\right)=3-\sqrt2+3\sqrt2-3=2\sqrt2\)
