c.
\(\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{6+2\sqrt{5}}=\left|\sqrt{5}-2\right|-\sqrt{\left(\sqrt{5}+1\right)^2}\)
\(=\sqrt{5}-2-\left|\sqrt{5}+1\right|=\sqrt{5}-2-\sqrt{5}-1\)
\(=-3\)
d.
\(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}-2\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=\left|\sqrt{3}+\sqrt{2}\right|+\left|\sqrt{3}-\sqrt{2}\right|-2\left|\sqrt{3}+1\right|\)
\(=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}-2\left(\sqrt{3}+1\right)\)
\(=2\sqrt{3}-2\sqrt{3}-2=-2\)
e.
\(A=\sqrt{6+2\sqrt{5}-\sqrt{\left(2\sqrt{5}-3\right)^2}}\)
\(=\sqrt{6+2\sqrt{5}-\left|2\sqrt{5}-3\right|}\)
\(=\sqrt{6+2\sqrt{5}-2\sqrt{5}+3}\)
\(=\sqrt{9}=3\)
