1) VT = \(\sqrt{12+2\sqrt{11}}-\sqrt{12-2\sqrt{11}}\)
\(\Leftrightarrow VT=\sqrt{\left(\sqrt{11}+1\right)^2}-\sqrt{\left(\sqrt{11}-1\right)^2}\)
\(\Leftrightarrow VT=\left(\sqrt{11}+1\right)-\left(\sqrt{11}-1\right)do\sqrt{11}>1\)
\(\Leftrightarrow VT=\sqrt{11}+1-\sqrt{11}+1\)
\(\Leftrightarrow VT=2=VP\left(đpcm\right)\)
2)
a)\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\)
\(=\left(\sqrt{5}-2\right)-\sqrt{5}\left(do\sqrt{5}>2\right)\)
\(=\sqrt{5}-2-\sqrt{5}=-2\)
b) \(\sqrt{3-2\sqrt{2}}-\sqrt{3+2\sqrt{2}}\)
\(=\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(\sqrt{2}+1\right)^2}\)
\(=\left(\sqrt{2}-1\right)-\left(\sqrt{2}+1\right)\left(do\sqrt{2}>1\right)\)
\(=\sqrt{2}-1-\sqrt{2}-1=-2\)
c)\(\sqrt{11-6\sqrt{2}}+3+\sqrt{2}\)
\(=\sqrt{\left(3-\sqrt{2}\right)^2}+3+\sqrt{2}\)
\(=\left(3-\sqrt{2}\right)+3+\sqrt{2}\left(do3>\sqrt{2}\right)\)
\(=3-\sqrt{2}+3+\sqrt{2}=6\)
d)\(\sqrt{7-2\sqrt{6}}+\sqrt{7+2\sqrt{6}}\)
\(=\sqrt{\left(\sqrt{6}-1\right)^2}+\sqrt{\left(\sqrt{6}+1\right)^2}\)
\(=\left(\sqrt{6}-1\right)+\left(\sqrt{6}+1\right)\left(do\sqrt{6}>1\right)\)
\(=\sqrt{6}-1+\sqrt{6}+1=2\sqrt{6}\)