\(\sqrt{10+2\sqrt{21}}+4\sqrt{\left(\sqrt{3}-\sqrt{7}\right)^2}\)
\(=\sqrt{(\sqrt{3})^2+2\sqrt{3}.\sqrt{7}+\left(\sqrt{7}\right)^2}+4\left|\sqrt{3}-\sqrt{7}\right|\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{7}\right)^2}+4\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{3}+\sqrt{7}+4\left(\sqrt{7}-\sqrt{3}\right)\)
\(=5\sqrt{7}-3\sqrt{3}\)