\(a,\sqrt{\left(2\sqrt{3}+3\right)}-\sqrt{\left(3-2\sqrt{3}\right)^2}\\ =\left|2\sqrt{3}+3\right|-\left|3-2\sqrt{3}\right|\\ =2\sqrt{3}+3-\left(2\sqrt{3}-3\right)\\ =2\sqrt{3}+3-2\sqrt{3}+3\\ =6\)
a, \(\sqrt{\left(2\sqrt{3}+3\right)^2}-\sqrt{\left(3-2\sqrt{3}\right)^2}\)
\(=\left|2\sqrt{3}+3\right|-\left|3-2\sqrt{3}\right|\)
\(=2\sqrt{3}+3-\left(-3+2\sqrt{3}\right)\)
\(=2\sqrt{3}+3+3-2\sqrt{3}\)
\(=6\)
b, \(\sqrt{\left(\sqrt{5}+2\right)^2}-\sqrt{9-4\sqrt{5}}\)
\(=\left|\sqrt{5}+2\right|-\sqrt{\left(\sqrt{5}-2\right)^2}\)
\(=\sqrt{5}+2-\sqrt{5}+2\)
\(=4\)
c, \(\left(2\sqrt{2}+3\right)\sqrt{\left(2\sqrt{2}-3\right)^2}-\sqrt{9+4\sqrt{2}}\)
\(=\left(2\sqrt{2}+3\right)\left(3-2\sqrt{2}\right)-\sqrt{\left(2\sqrt{2}+1\right)^2}\)
\(=9-8-2\sqrt{2}-1\)
\(=-2\sqrt{2}\)
d, \(\left(2\sqrt{5}-3\right)\sqrt{29+12\sqrt{5}}+11\sqrt{3-2\sqrt{2}}\)
\(=\left(2\sqrt{5}-3\right)\sqrt{\left(2\sqrt{5}+3\right)^2}+11\sqrt{\left(\sqrt{2}-1\right)^2}\)
\(=\left(2\sqrt{5}-3\right)\left(2\sqrt{5}+3\right)+11\left|\sqrt{2}-1\right|\)
\(=20-9+11\sqrt{2}-11\)
\(=11\sqrt{2}\)
