化简：\(\sqrt{10 + 8\sqrt{3 + 2\sqrt{2}}}\)
要计算\(\sqrt{10 + 8\sqrt{3 + 2\sqrt{2}}}\)，可以从最内层的嵌套根式开始逐步化简，通过观察和配方法将根式转化为完全平方的形式。
化简：\(\sqrt{10 + 8\sqrt{3 + 2\sqrt{2}}}\)
=\(\sqrt{10 + 8\sqrt{2 + 2\sqrt{2}+1}}\)
=\(\sqrt{10 + 8\sqrt{(\sqrt{2}+1)^2}}\)
=\(\sqrt{10 + 8(\sqrt{2}+1)}\)
=\(\sqrt{10 + 8\sqrt{2}+8}\)
=\(\sqrt{2 + 8\sqrt{2}+16}\)
=\(\sqrt{(\sqrt{2}+4)^2}\)
=\(\sqrt{2}+4\)