1:
a) Ta có: \(\sqrt{\left(2\sqrt{2}-3\right)^2}+\sqrt{11+6\sqrt{2}}\)
\(=\left|2\sqrt{2}-3\right|+\sqrt{9+2\cdot3\cdot\sqrt{2}+2}\)
\(=3-2\sqrt{2}+\sqrt{\left(3+\sqrt{2}\right)^2}\)(vì \(3>2\sqrt{2}\))
\(=3-2\sqrt{2}+3+\sqrt{2}\)(vì \(3>\sqrt{2}>0\))
\(=6-\sqrt{2}\)
b) Ta có: \(\sqrt{29-12\sqrt{5}}-\sqrt{29+12\sqrt{5}}\)
\(=\sqrt{20-2\cdot\sqrt{20}\cdot3+9}-\sqrt{20+2\cdot\sqrt{20}\cdot3+9}\)
\(=\sqrt{\left(2\sqrt{5}-3\right)^2}-\sqrt{\left(2\sqrt{5}+3\right)^2}\)
\(=2\sqrt{5}-3-\left(2\sqrt{5}+3\right)\)(vì \(2\sqrt{5}>3>0\))
\(=2\sqrt{5}-3-2\sqrt{5}-3\)
=-6
c) Ta có: \(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)
\(=\sqrt{7-2\cdot\sqrt{7}\cdot1+1}-\sqrt{7+2\cdot\sqrt{7}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(=\sqrt{7}-1-\left(\sqrt{7}+1\right)\)(vì \(\sqrt{7}>1>0\))
\(=\sqrt{7}-1-\sqrt{7}-1\)
=-2
