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