\(F=\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{\left(\sqrt{5}-2\right)^2}=\left|\sqrt{5}+1\right|-\left|\sqrt{5}-2\right|\)
\(=\sqrt{5}+1-\sqrt{5}+2=3\)
\(G=\dfrac{\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}+\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}=\sqrt{6}+\sqrt{5}\)
\(H=\dfrac{10\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\dfrac{55\left(2\sqrt{3}-1\right)}{\left(2\sqrt{3}-1\right)\left(2\sqrt{3}+1\right)}=5\left(\sqrt{3}+1\right)-5\left(2\sqrt{3}-1\right)\)
\(=5\sqrt{3}+5-10\sqrt{3}+5=10-5\sqrt{3}\)
\(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
\(=\sqrt{5}+1-\sqrt{5}+2\)
=3
