\(=\sqrt{3+7+5+2\sqrt{15}+2\sqrt{35}+2\sqrt{21}}\)
\(=\sqrt{\sqrt{3}^2+\sqrt{5}^2+\sqrt{7}^2+2\sqrt{3.5}+2\sqrt{5.7}+2\sqrt{3.7}}\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{5}+\sqrt{7}\right)^2}\)
\(=\sqrt{3}+\sqrt{5}+\sqrt{7}\)
\(\Rightarrow m^2+n^2+p^2=3^2+5^2+7^2=83\)
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